All Questions
Tagged with floer-homology reference-request
7 questions
11
votes
2
answers
444
views
Fredholm property about $L^p$-extension $(p\neq 2)$ of differential operators
The following is a well-known result for elliptic operators.
Theorem. Let $P: \Gamma(E)\to \Gamma(F)$ be an elliptic operator of order $m$ between vector bundles $E$ and $F$ over a compact ...
- 2,789
9
votes
1
answer
545
views
Citation hunting: Floer on spectral sequences
I vaguely remember a YouTube talk that began with a citation from Floer regarding the existence of a spectral sequence. The idea was that given a manifold with a Morse function, we can construct a ...
- 193
8
votes
0
answers
251
views
Exact triangle for monopole Floer homology with $\mathbb{Z}$-coefficient
Let $Y$ be oriented 3 manifold with torus boundary and let $\gamma_{j}$ (j=0,1,2) be three curves on its boundary with $\#(\gamma_{j}\cap \gamma_{j+1})=-1$. We denote by $Y_{j}$ the manifold obtained ...
- 1,069
5
votes
2
answers
371
views
Manifold of mappings between $M$ and $N$, with non-compact source $M$
EDIT: Let $M$ and $N$ are two smooth manifold and suppose $N$ is compact but $M$ is not necessarily compact. For my purpose, I just need to consider the case $M=\mathbb R \times S^1$ or $\mathbb R \...
- 2,789
3
votes
0
answers
233
views
Locality in Floer theory
There appears to be a dearth of resources and references for the question of 'locality' in Floer theory. In particular, I cannot seem to find any complete statement of what people refer to as '...
- 31
2
votes
0
answers
237
views
Parametric Sard-Smale theorem - when is the generic set open?
I am learning Morse/Floer Theory and in my work on my master's thesis I want to apply the parametric Sard-Smale theorem. I.e. I consider a Banach bundle $\mathcal{L} \to \mathcal{M}\times \mathcal{G}$ ...
- 529
1
vote
1
answer
247
views
Maslov index equal to $2$ implies that the disk is not multiply covered
In the paper Floer cohomology of lagrangian intersections and pseudo-holomorphic disks in page $1009$ the authors claim that a map $w:D^2\rightarrow S^2$ with $w|_{\partial D^2}\subset L$, where $L$ ...
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