Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Patrick Orson"'
Publikováno v:
Advances in Mathematics, 2022, Vol.409(Part B), pp.108665 [Peer Reviewed Journal]
We describe a calculus of moves for modifying a framed flow category without changing the associated stable homotopy type. We use this calculus to show that if two framed flow categories give rise to the same stable homotopy type of homological width
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f341c83c637e936f3f153722f4f0f76
https://doi.org/10.1016/j.aim.2022.108665
https://doi.org/10.1016/j.aim.2022.108665
Publikováno v:
Indiana University Mathematics Journal. 69:2505-2547
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d8b5d4032e85d469245e015d6abddb0
https://doi.org/10.1512/iumj.2020.69.8081
https://doi.org/10.1512/iumj.2020.69.8081
The s-cobordism theorem, the sphere embedding theorem, and the Poincaré conjecture comprise three key consequences of the disc embedding theorem. The chapter begins by explaining in detail how to use the disc embedding theorem to prove the 5-dimensi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04efa1c6ec83c1af3f3461f96a095218
https://doi.org/10.1093/oso/9780198841319.003.0020
https://doi.org/10.1093/oso/9780198841319.003.0020
‘The Whitehead Decomposition’ introduces this historically significant decomposition. Not only is the quotient of the 3-sphere by the Whitehead decomposition not homeomorphic to the 3-sphere, it is not even a manifold. In order to detect this cur
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b67102caa2934df7a6a4c4076a2b6afa
https://doi.org/10.1093/oso/9780198841319.003.0007
https://doi.org/10.1093/oso/9780198841319.003.0007
Surgery theory and the classification of simply connected 4-manifolds comprise two key consequences of the disc embedding theorem. The chapter begins with an introduction to surgery theory from the perspective of 4-manifolds. In particular, the terms
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b2b89b15cd3614726244791854d5d384
https://doi.org/10.1093/oso/9780198841319.003.0022
https://doi.org/10.1093/oso/9780198841319.003.0022
Open problems in the study of topological 4-manifolds are explained in detail. An important open problem is to determine whether the disc embedding theorem and its antecedents hold for all groups; in other words, whether all groups are good. The disc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8cea16d354ccb20c7ce2429ac672138c
https://doi.org/10.1093/oso/9780198841319.003.0023
https://doi.org/10.1093/oso/9780198841319.003.0023
Good groups are defined in terms of whether capped gropes of height 1.5 contain certain types of immersed discs. The disc embedding theorem holds for 4-manifolds with good fundamental group. It is proven that the infinite cyclic group and finite grou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2ddfc2fbb18ee36914172795a6fad849
https://doi.org/10.1093/oso/9780198841319.003.0019
https://doi.org/10.1093/oso/9780198841319.003.0019
Publikováno v:
The Disc Embedding Theorem
‘Shrinking Starlike Sets’ presents a proof that null decompositions with recursively starlike-equivalent elements shrink. Unlike in previous chapters, the shrink is produced abstractly rather than explicitly. The chapter proceeds in steps, first
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d002505a5e291f894ecd74549800db8
https://doi.org/10.1093/oso/9780198841319.003.0009
https://doi.org/10.1093/oso/9780198841319.003.0009
Publikováno v:
Compositio Mathematica
Compositio Mathematica, 2021, Vol.157(10), pp.2242-2279 [Peer Reviewed Journal]
Compositio Mathematica, 157 (10)
Compositio Mathematica, 2021, Vol.157(10), pp.2242-2279 [Peer Reviewed Journal]
Compositio Mathematica, 157 (10)
The trace of the -framed surgery on a knot in is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded -sphere whose complement ha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1b789d9aa3d7d4ff47f47f6f511f83a
https://hdl.handle.net/21.11116/0000-0009-7CA2-521.11116/0000-0009-7CA4-321.11116/0000-0009-7CA5-2
https://hdl.handle.net/21.11116/0000-0009-7CA2-521.11116/0000-0009-7CA4-321.11116/0000-0009-7CA5-2
Publikováno v:
Experimental mathematics, 2020, Vol.29(4), pp.475-500 [Peer Reviewed Journal]
The Lipshitz-Sarkar stable homotopy link invariant defines Steenrod squares on the Khovanov cohomology of a link. Lipshitz-Sarkar constructed an algorithm for computing the first two Steenrod squares. We develop a new algorithm which implements the f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92646f8a16bf3a7da9ea7745e822cf24
http://dro.dur.ac.uk/25161/
http://dro.dur.ac.uk/25161/