The topology tag has no wiki summary.
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1answer
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Topological vs. non-topological noetherian charges
What (if any) is the relationship between the conserved (non-topological) noetherian charges and topological charges? Namely, is there any "generalization" of the Noether's first theorem that includes ...
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2answers
161 views
Excluding big bang itself, does spacetime have a boundary?
My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity).
Does this mean that ...
6
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1answer
131 views
Our Universe Can't be Looped? [duplicate]
With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
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1answer
61 views
Consequences of Compactness in Physics
If we understand spacetime as a $4$-dimensional manifold $M$, from the point of view of physics what are the consquences of a subset of it being compact? My point here is simple: in math we usually ...
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2answers
81 views
Are all points in the universe connected?
Is it true that every point in the universe is connected or could be so theoretically? If so how is this mediated?
Is it through the quantum nature of the fabric of space or is it through the ...
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0answers
59 views
Do we expect that the universe is simply-connected? [duplicate]
I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the ...
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1answer
45 views
Topological phase transitions - breaking of continuous translational invariance [closed]
I'm relatively new to the theoretical side of physics. I have a question about topology, continuous symmetry breaking and phase transitions. Your help is much appreciated!
Ok so I have an infinite ...
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0answers
113 views
Tangent bundles and $\mathbb{C}P^n$ and $\mathbb{C}^n$
As discussed here the complex projective space $\mathbb{C}P^n$ is the set of all lines on $\mathbb{C}^n$ passing through the origin. It would seem natural to assume that any $\mathbb{C}P^n$ can be ...
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1answer
104 views
Topology for physicists [duplicate]
Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
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1answer
102 views
How is the direction of time determined in general relativity?
In special relativity every frame has its own unique time axis, represented in Minkowski diagrams by a fan-out of time vectors that grows infinitely dense as you approach the surface of the light cone ...
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1answer
176 views
Chiral edge state as topological properity of bulk state
As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, ...
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1answer
64 views
Proof of quantization of magnetic charge of monopoles using homotopy groups
Suppose we place a monopole at the origin $\{{\bf 0}\}$, and the gauge field is well-definded in region $\mathbb R^3-\{0\}$ which is homomorphic to a sphere $S^2$.
Then the total manifold is $U(1)$ ...
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1answer
205 views
Quantum dimension in topological entanglement entropy
In 2D the entanglement entropy of a simply connected region goes like
\begin{align}
S_L \to \alpha L - \gamma + \cdots,
\end{align}
where $\gamma$ is the topological entanglement entropy.
$\gamma$ is ...
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1answer
230 views
First Chern number, monoples and quantum Hall states
The first Chern number $\cal C$ is known to be related to various physical objects.
Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to ...
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1answer
82 views
Gauss-Bonnet theorem in the Hawking/Ellis book
At the page 336 of Hawking, Ellis: The Large Scale Structure of Space-Time, the Gauss-Bonnet theorem is stated as
$$\int_H \hat{R}\ d\hat{S} = 2\pi \chi(H) \qquad (1)$$
with
$$\hat{R} = R_{abcd} ...
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0answers
115 views
Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?
A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
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1answer
240 views
Questions about Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper
I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I ...
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2answers
209 views
Topology and Quantum mechanics
I have a very simple question. Can we know about the topology of the underlying space-time manifolds from Quantum mechanics calculations? If the Space-time is not simply connected, how can one measure ...
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1answer
168 views
What is the simplest possible topological Bloch function?
Kohmoto (1985) pointed out in Topological Invariant and the Quantization of the Hall Conductance how TKNN's calcuation of Hall conducance is related to topology, in which topologically nontriviality ...
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0answers
89 views
Alternate geodesic completions of a Schwarzschild black hole
The Kruskal-Szekeres solution extends the exterior Schwarzschild solution maximally, so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction.
...
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1answer
209 views
+300
Does a charged or rotating black hole change the genus of spacetime?
For a Reissner–Nordström or Kerr black hole there is an analytic continuation through the event horizon and back out. Assuming this is physically meaningful (various site members hereabouts think ...
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3answers
259 views
Could metric expansion create holes, or cavities in the fabric of spacetime?
Is it possible for metric expansion to create holes, or cavities in the fabric of spacetime?
According to the Schwarzschild metric, the metric expansion of space around a black hole goes to infinity ...
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1answer
80 views
Proper times of two observers in a three-torus
Consider two observer in a tree-torus space of size $L$. Observer $A$ is at rest, while observer $B$ moves in the $x$-direction with constant velocity $v$. $A$ and $B$ began at the same event, and ...
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3answers
338 views
Homotopy $\pi_4(SU(2))=\mathbb{Z}_2$
Recently I read a paper using $$\pi_4(SU(2))=\mathbb{Z}_2.$$ Do you have any visualization or explanation of this result?
More generally, how do physicists understand or calculate high dimension ...
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0answers
141 views
Lagrangian for Goldstone mode + topological excitation
The XY-model Hamiltonian is the following,
$${\cal H}~=~-J\sum_{\langle i,j\rangle} \cos (\theta_i -\theta_j).$$
The Goldstone mode corresponds to term $(\nabla \theta)^2$ in the effective ...
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2answers
415 views
How is the topological $Z_2$ invariant related to the Chern number? (e.g. for a topological insulator)
This question relates to the $Z_2$ invariant defined e.g. for topological insulators:
Is it correct to relate $Z_2$ = 1 to an odd Chern number and $Z_2$ = 0 to an even Chern number?
If yes, is it ...
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1answer
317 views
Chern number in condensed matter physics
In mathematics, the Chern number is defined in terms of the Chern class of a manifold. What is the exact definition of Chern number in condensed matter physics, i.e. quantum hall system?
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2answers
262 views
(Co)homology of the universe
In this post let $U$ be the universe considered as a manifold.
From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
3
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1answer
171 views
Is a preferred reference frame of the universe the old aether?
About two years ago I posted a question about a symmetrical twin paradox: Here.
Recently a new answer was posted and an intense discussion ensued: Here.
One of the points discussed concerns a ...
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0answers
140 views
7 sphere, is there any physical interpretation of exotic spheres?
Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately:
homeomorphic but not diffeomorphic to the standard Euclidean n-sphere
The first exotic ...
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5answers
127 views
Why is the world sheet of an open string a cylinder?
I went to a lecture a few weeks ago and was told the following:
The world sheet of a closed string is a normal, standing cylinder.
The world sheet of an open string is a cylinder on its side.
This ...
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1answer
129 views
Can closed loops evade the spin-statistic theorem in 3 dimensions?
The famous spin-statistics result asserts that there are only bosons and fermions, and that they have integer and integer-and-a-half spin respectively. In two-dimensional condensed matter systems, ...
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1answer
171 views
Large gauge transformations
I would like to understand what is the importance of large gauge transformations. I read that these gauge transformation cannot be deformed to the identity, but why should we care about that?
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2answers
124 views
Graph Invariants and Statistical Mechanics
Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was ...
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1answer
282 views
What is topological degeneracy in condensed matter physics?
What is topological degeneracy in strongly correlated systems such as FQH?
What is the difference between topological degeneracy and ordinary degeneracy?
Why is topological degeneracy important for ...
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1answer
99 views
Why are topological solitons present in some phases for lattice models?
Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
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2answers
126 views
Is a compact universe consistent with the results of (for example) the Michelson-Morley experiment?
If the universe is compact then there is a twin paradox that is resolvable only by selecting a preferred inertial reference frame (arXiv). I was under the impression that the lack of a preferred ...
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2answers
361 views
Aharonov-Bohm Effect and Flux Quantization in superconductors
Why is the magnetic flux not quantized in a standard Aharonov-Bohm (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?
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2answers
246 views
On Aharonov–Bohm effect
Aharonov–Bohm effect in brief is due to some singularities in space. In books it's infinite solenoid most of the time, which makes some regions of space not simply connected.
What intrigues me is the ...
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1answer
98 views
how does nature prevent transient toroidal event horizons?
.. and does it really need to?
Steps to construct a (transient) toroidal event horizon in a asymptotically flat Minkowski spacetime:
1) take a circle of radius $R$
2) take $N$ equidistant points in ...
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1answer
113 views
what is wrong with the following argument about stokes law in compact universes?
I want to understand what is wrong with the following argument:
in a topologically compact spacetime, a closed 3D boundary separates the spacetime in two connected components, because of this ...
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0answers
69 views
are pinch-off bubbles valid solutions to general relativity?
are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and ...
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3answers
181 views
What are some mechanics examples with a globally non-generic symplecic structure?
In the framework of statistical mechanics, in books and lectures when the fundamentals are stated, i.e. phase space, Hamiltons equation, the density etc., phase space seems usually be assumed to be ...
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1answer
117 views
geometry inside the event horizon
I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a schwarszchild black hole. I would appreciate any insights or corrections to the above.
...
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4answers
477 views
Topology needed for Differential Geometry [duplicate]
I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from ...
4
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2answers
342 views
Book covering Topology required for physics and applications
I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
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1answer
83 views
Does General Relativity require that Spacetime must be a orientable? [duplicate]
Possible Duplicate:
Can spacetime be non-orientable?
Apart from the constraints put on the topology of spacetime by QFT (Parity For example), if the global topology of a universe is that of ...
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0answers
127 views
What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?
What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
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1answer
206 views
What is the fate of a 3-Torus universe?
Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?
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2answers
341 views
Does spacetime in general relativity contain holes?
Are there physical models of spacetimes, which have bounded (four dimensional) holes in them?
And do the Einstein equations give restrictions to such phenomena?
Here by holes I mean ...
