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Naturality and Mapping Class Groups in Heegard Floer Homology

Andras Juhasz
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      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.
      Format: Paperback / softback CONTRIBUTORS: Andras Juhasz EAN: 9781470449728 COUNTRY: United States PAGES: WEIGHT: 332 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2022-05-01 CITY: GENRE: MATHEMATICS / General WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

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      Andras Juhasz, University of Oxford, United Kingdom.Dylan P. Thurston, Indiana University, Bloomington.Ian Zemke, Princeton University, NJ.
      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.
      Format: Paperback / softback CONTRIBUTORS: Andras Juhasz EAN: 9781470449728 COUNTRY: United States PAGES: WEIGHT: 332 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2022-05-01 CITY: GENRE: MATHEMATICS / General WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

      Customer Reviews

      Be the first to write a review
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      Andras Juhasz, University of Oxford, United Kingdom.Dylan P. Thurston, Indiana University, Bloomington.Ian Zemke, Princeton University, NJ.

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