|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Higher rank local systems in Lagrangian Floer theory | | Momchil Konstantinov
; | | Date: |
13 Jan 2017 | | Abstract: | We extend Floer theory for monotone Lagrangians to allow coefficients in
local systems of arbitrary rank. Unlike the rank 1 case, this is often
obstructed by Maslov 2 discs. We study exactly what the obstruction is and
define some natural unobstructed subcomplexes. To illustrate these
constructions we do some explicit calculations for the Chiang Lagrangian
$L_{Delta} subseteq mathbb{C}P^3$. For example, we equip $L_{Delta}$ with a
particular rank 2 local system $W$ over the field with 2 elements such that the
resulting Floer complex $CF^*(W,W)$ is unobstructed despite the presence of
Maslov 2 discs. We compute that the cohomology $HF^*(W,W)$ is non-zero and
deduce that the Chiang Lagrangian cannot be disjoined from $mathbb{R}P^3$ by a
Hamiltonian isotopy. | | Source: | arXiv, 1701.3624 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER