Naturality and Mapping Class Groups in Heegard Floer Homology
Book Details
Format
Paperback / Softback
Book Series
Memoirs of the American Mathematical Society
ISBN-10
1470449722
ISBN-13
9781470449728
Publisher
American Mathematical Society
Imprint
American Mathematical Society
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Mar 30th, 2022
Weight
336 grams
Dimensions
17.70 x 25.20 x 1.50 cms
Ksh 13,150.00
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Demonstrates that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural - they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold. Furthermore, the authors functorially assign isomorphisms to diffeomorphisms, and show that this assignment is isotopy invariant.
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.
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