Naturality and Mapping Class Groups in Heegard Floer Homology
Regular price
€85.99
14 days return policy
Shipping & Delivery
A01=Andras Juhasz
A01=Dylan P. Thurston
A01=Ian Zemke
Author_Andras Juhasz
Author_Dylan P. Thurston
Author_Ian Zemke
Category=PBM
Category=PBP
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Product details
- ISBN 9781470449728
- Weight: 332g
- Dimensions: 178 x 254mm
- Publication Date: 30 Mar 2022
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
Secure
checkout
Fast Shipping
Easy returns
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show that this assignment is isotopy invariant.
The proof relies on finding a simple generating set for the fundamental group of the "space of Heegaard diagrams," and then showing that Heegaard Floer homology has no monodromy around these generators. In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds.
The proof relies on finding a simple generating set for the fundamental group of the "space of Heegaard diagrams," and then showing that Heegaard Floer homology has no monodromy around these generators. In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds.
Andras Juhasz, University of Oxford, United Kingdom.
Dylan P. Thurston, Indiana University, Bloomington.
Ian Zemke, Princeton University, NJ.
Dylan P. Thurston, Indiana University, Bloomington.
Ian Zemke, Princeton University, NJ.
