Localization for Involutions in Floer Cohomology

By P. Seidel, I. Smith. 2010

78 citations recorded by the source corpus.

We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/dc7f21ed5ca6fe38067a520108fb9a57ff83aaf5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. P. Seidel
2. A. Oancea
3. Frederick J. Bourgeois III
4. M. Abouzaid
5. Kristen Hendricks
6. Jake Solomon
7. I. Smith
8. Mark McLean

In Mathematical Physics

1. A. Oancea
2. P. Seidel
3. Frederick J. Bourgeois III
4. M. Abouzaid
5. Jake Solomon
6. Kristen Hendricks
7. Mark McLean
8. Alexander F. Ritter

In Neurology

1. Kristen Hendricks
2. Ciprian Manolescu
3. P. Seidel
4. Ian Zemke
5. Jennifer Hom
6. Peter S. Ozsv'ath
7. Zolt'an Szab'o
8. A. Stipsicz

Citations in the corpus

• Symplectic Cohomology and q-Intersection Numbers (2010, background): “In fact, this is precisely the differential used to define S(1)-equivariant Floer cohomology (see again [43] or [36]; for additional foundational material about equivariant Floer cohomology theories see [18, 40]; an analytically more demanding approach is presented in [8]).”
• Involutive Heegaard Floer homology (2015, methodology): “In order to understand what a potential Z2-equivariant version of HF +(Y ) (or “Pin(2) Heegaard Floer homology”) would look like, recall that a model for constructing Z2-equivariant Floer homology (in a different setting) was given by Seidel and Smith [53].”
• $S^1$-equivariant symplectic homology and linearized contact homology (2012, background): “[42, 55, 57] Let f : CP → R be a Morse function and f̃ : S → R be its S(1)-invariant lift.”