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Results tagged with vector-bundles
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user 402
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
9
votes
Obstructions to the existence of a flat connection on a vector bundle
A $d$-dimensional flat real vector bundle $E→M$ is classified by a map $\def\B{{\sf B}}\def\GL{{\rm GL}}M→\B\GL(d)_δ$, where $\GL(d)_δ$ is the orthogonal group equipped with the discrete topology.
Arb …
- 37.8k
5
votes
Accepted
Existence parallel vector fields and its effect on the topology of manifolds (Karp's Thesis)
The full text of Karp's thesis (a scanned PDF file) is available here:
https://search.proquest.com/pqdtglobal/docview/302809402/
- 37.8k
5
votes
1d TQFT minus connection =?
Going into more detail (and consequently making more and more mistakes), a vector bundle with connection allows to assign to a point the fibre over that point, and to a path the monodromy (or holon …
- 37.8k
3
votes
Accepted
Reference for $E_{\infty}$-ness of the Chern Character
The answer really depends on one's desired choice of definitions for KU, HQ, and the Chern character itself;
some definitions allow one to produce a very short definition of the Chern character as an …
- 37.8k
15
votes
what is a spinor structure?
A spin structure on a real vector space V equipped with a real quadratic form μ
is an invertible bimodule (i.e., a Morita equivalence)
from Cl(V,μ) to Cl(Rdim(V),ν).
Here ν is the direct sum of dim(V) …
- 37.8k