Tagged Questions
2
votes
1answer
62 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 ...
1
vote
1answer
107 views
Topology for physicists [duplicate]
Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
4
votes
1answer
232 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 ...
13
votes
3answers
339 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 ...
2
votes
2answers
263 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 ...
4
votes
0answers
141 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 ...
1
vote
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 ...
3
votes
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
votes
2answers
345 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 ...
2
votes
0answers
129 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 & ...
8
votes
3answers
48 views
Does the complex 3-sphere have a complex structure modulus?
This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical ...
5
votes
0answers
33 views
What is the importance of studying degeneration on $M_g$
Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$.
It seems to be important in physics to study ...
9
votes
5answers
196 views
Where do theta functions and canonical Green functions appear in physics
In the beginning of Section 5 in his article, Wentworth mentions a result of Bost and proves it using the spin-1 bosonization formula. This result provides a link between theta functions, canonical ...
11
votes
2answers
335 views
The entropic cost of tying knots in polymers
Imagine I take a polymer like polyethylene, of length $L$ with some number of Kuhn lengths $N$, and I tie into into a trefoil knot. What is the difference in entropy between this knotted polymer and ...
0
votes
1answer
167 views
A question on smooth 1-manifolds
Consider two people living on two different smooth 1-manifolds $S$ and $T$ as shown in figure 1. The manifold $S$ is a bump function joining the points $A$ and $B$ and the manifold $T$ is formed by ...
13
votes
7answers
2k views
Applications of Algebraic Topology to physics
I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most ...
