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Topologically trivial proper 2-knots Gompf, Bob
Description
We will discuss the knot theory of proper embeddings of the plane and half-open annulus in $\mathbb{R}^4$, focusing on what is arguably the simplest situation that is intrinsically noncompact. While it is still unknown if a smoothly knotted embedding $S^2\to\mathbb{R}^4$ can be topologically unknotted, there are various ways of realizing the analogous phenomenon for planes and annuli. We will show how to construct and distinguish various families of examples. These can exhibit remarkably different behavior, and can sometimes be explicitly drawn with level diagrams.
Item Metadata
Title |
Topologically trivial proper 2-knots
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-11-06T10:21
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Description |
We will discuss the knot theory of proper embeddings of the plane and half-open annulus in $\mathbb{R}^4$, focusing on what is arguably the simplest situation that is intrinsically noncompact. While it is still unknown if a smoothly knotted embedding $S^2\to\mathbb{R}^4$ can be topologically unknotted, there are various ways of realizing the analogous phenomenon for planes and annuli. We will show how to construct and distinguish various families of examples. These can exhibit remarkably different behavior, and can sometimes be explicitly drawn with level diagrams.
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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: University of Texas Austin
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Series | |
Date Available |
2020-05-05
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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 |
10.14288/1.0390352
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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 Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International