7
$\begingroup$

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or other resource). Explain what the resource is like as much as you can; that way the reader can decide which one is most suited for them rather than relying on the suggestions of others. Answers which just suggest a book or paper may be deleted.

Also note that all answers to this question are automatically community-owned, so they are often subject to major editing, often to make them comply with the book policy.

I am now going through Isham's book Modern differential geometry for physicists and got stuck with the notions of etale bundle, presheaf and sheaf. Could someone please suggest some other, more intuitive and more accessible references on etale bundles and sheaves, preferably the ones giving more motivation and sufficiently many explicit (and worked-out) examples and, preferably, accessible to theoretical physicists (i.e., not just mathematicians)?

P.S. To make things clear, a few math texts I have managed to find so far like Godement's and Bredon's Sheaf Theory (two books with the same title) seem way too tough for me. The part on sheaves in Arapura's Algebraic Geometry over Complex Numbers is somewhat better but still a bit too fast going and with too few examples and not too much motivation. Pretty much the same applies to the part on sheaves (which is too brief anyway) in the Clay Institute volume Mirror Symmetry. If there are no suitable books, are there perhaps some good lecture notes on the subject accessible to physicists rather than just mathematicians, from which one get a reasonable intuition on sheaves and stuff?

$\endgroup$
0

1 Answer 1

10
$\begingroup$

Here is a motivation for the general notion of sheaf and sheaf cohomology:

A general introduction to differential geometry as needed in physics in terms of sheaves is at

More along these lines is in section 1.2 of arXiv:1310.7930, which describes physics in terms of sheaves (and higher sheaves) on smooth manifolds (and variants thereof).

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.