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Handle decompositions of the 4-sphere, Generalized Property R, and trisections Zupan, Alex
Description
Waldhausen's Theorem implies that any handle decomposition of the 3-sphere can be simplified without introducing additional handles. The analogue in dimension 4 is unknown, but it is widely believed that there are handle decompositions of the standard smooth 4-sphere which require additional pairs of canceling handles before they admit simplification. For handle decompositions without 1-handles, it suffices to understand links in the 3-sphere with certain Dehn surgeries these are the links characterized by the Generalized Property R Conjecture and its variations. We show that a given link has Stable Generalized Property R if and only if a certain infinite family of induced trisections is nonstandard; thus, we provide evidence that trisections may be used to verify that the potential counterexamples introduced by Gompf-Scharlemann-Thompson do not have Stable Generalized Property R. Parts of this talk are joint with Jeffrey Meier and Trenton Schirmer.
Item Metadata
Title |
Handle decompositions of the 4-sphere, Generalized Property R, and trisections
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-02-26T09:59
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Description |
Waldhausen's Theorem implies that any handle decomposition of the 3-sphere can be simplified without introducing additional handles. The analogue in dimension 4 is unknown, but it is widely believed that there are handle decompositions of the standard smooth 4-sphere which require additional pairs of canceling handles before they admit simplification. For handle decompositions without 1-handles, it suffices to understand links in the 3-sphere with certain Dehn surgeries these are the links characterized by the Generalized Property R Conjecture and its variations.
We show that a given link has Stable Generalized Property R if and only if a certain infinite family of induced trisections is nonstandard; thus, we provide evidence that trisections may be used to verify that the potential counterexamples introduced by Gompf-Scharlemann-Thompson do not have Stable Generalized Property R. Parts of this talk are joint with Jeffrey Meier and Trenton Schirmer.
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Extent |
56 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Nebraska-Lincoln
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Series | |
Date Available |
2016-08-27
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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 |
10.14288/1.0313303
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International