The collar adding lemma
The collar adding lemma
The collar adding lemma is a key ingredient in the proof of the disc embedding theorem. Specifically, it proves that a skyscraper with an added collar is homeomorphic to the standard 4-dimensional 2-handle. The proof is similar to the proof in a previous chapter that the Alexander gored ball with an added collar is homeomorphic to the standard 3-ball. Roughly speaking, a skyscraper is seen as the quotient space of the 4-ball corresponding to a certain decomposition. The added collar allows the decomposition to be modified so that the resulting decomposition shrinks; that is, the corresponding quotient space, which is identified with the skyscraper with an added collar, is homeomorphic to the original 4-ball.
391-394
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
Ray, Arunima
83cc0cbe-d85d-46f1-90ea-e67bc44386b8
20 July 2021
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
Ray, Arunima
83cc0cbe-d85d-46f1-90ea-e67bc44386b8
Kasprowski, Daniel, Powell, Mark and Ray, Arunima
(2021)
The collar adding lemma.
In,
Behrens, Stefan, Kalmar, Boldizsar, Kim, Min Hoon, Powell, Mark and Ray, Arunima
(eds.)
The Disc Embedding Theorem.
Oxford University Press, .
(doi:10.1093/oso/9780198841319.003.0025).
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Abstract
The collar adding lemma is a key ingredient in the proof of the disc embedding theorem. Specifically, it proves that a skyscraper with an added collar is homeomorphic to the standard 4-dimensional 2-handle. The proof is similar to the proof in a previous chapter that the Alexander gored ball with an added collar is homeomorphic to the standard 3-ball. Roughly speaking, a skyscraper is seen as the quotient space of the 4-ball corresponding to a certain decomposition. The added collar allows the decomposition to be modified so that the resulting decomposition shrinks; that is, the corresponding quotient space, which is identified with the skyscraper with an added collar, is homeomorphic to the original 4-ball.
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Published date: 20 July 2021
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Local EPrints ID: 475477
URI: http://eprints.soton.ac.uk/id/eprint/475477
PURE UUID: 356f32c2-0ae2-4d15-978f-7d4e3e45b001
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Date deposited: 20 Mar 2023 17:40
Last modified: 17 Mar 2024 04:19
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Contributors
Author:
Daniel Kasprowski
Author:
Mark Powell
Author:
Arunima Ray
Editor:
Stefan Behrens
Editor:
Boldizsar Kalmar
Editor:
Min Hoon Kim
Editor:
Mark Powell
Editor:
Arunima Ray
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