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Knot Floer homology as immersed curves Hanselman, Jonathan
Description
I will describe how the knot Floer homology of a knot K can be represented by a decorated collection of immersed curves in the marked torus. The surgery formula for knot Floer homology translates nicely to this setting: the Heegaard Floer homology HF^- of p/q surgery on K is given by the Lagrangian Floer homology of these immersed curves with a line of slope p/q. For a simplified â UV = 0â version of knot Floer homology, the analogous statements follow from earlier work with Rasmussen and Watson by passing through the bordered Floer homology of the knot complement, but a more direct approach allows us to capture the stronger â minusâ invariant by adding decorations to the curves. Often recasting algebraic structures in terms of geometric objects in this way leads to new insights and results; I will mention some applications of this immersed curves framework, including obstructions to cosmetic surgeries.
Item Metadata
Title |
Knot Floer homology as immersed curves
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-06-12T08:02
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Description |
I will describe how the knot Floer homology of a knot K can be represented by a decorated collection of immersed curves in the marked torus. The surgery formula for knot Floer homology translates nicely to this setting: the Heegaard Floer homology HF^- of p/q surgery on K is given by the Lagrangian Floer homology of these immersed curves with a line of slope p/q. For a simplified â UV = 0â version of knot Floer homology, the analogous statements follow from earlier work with Rasmussen and Watson by passing through the bordered Floer homology of the knot complement, but a more direct approach allows us to capture the stronger â minusâ invariant by adding decorations to the curves. Often recasting algebraic structures in terms of geometric objects in this way leads to new insights and results; I will mention some applications of this immersed curves framework, including obstructions to cosmetic surgeries.
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Extent |
55.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Princeton University
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Series | |
Date Available |
2020-12-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0395258
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International