Dual decompositions of 4-manifolds III: s-cobordisms

Autor:	Frank Quinn
Rok vydání:	2006
Předmět:	Combinatorics 4-manifold Applied Mathematics General Mathematics Homotopy Boundary structure Diffeomorphism Invariant (mathematics) Mathematics::Symplectic Geometry Mathematics::Geometric Topology Mathematics::Algebraic Topology Triviality Mathematics
Zdroj:	Transactions of the American Mathematical Society. 359:1433-1443
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-06-03917-1
Popis:	The main result is that an s-cobordism (topological or smooth) of 4-manifolds has a product structure outside a “core” sub-s-cobordism. These cores are arranged to have quite a bit of structure, for example they are smooth and abstractly (forgetting boundary structure) diffeomorphic to a standard neighborhood of a 1-complex. The decomposition is highly nonunique so cannot be used to define an invariant, but it shows that the topological s-cobordism question reduces to the core case. The simply-connected version of the decomposition (with 1-complex a point) is due to Curtis, Freedman, Hsiang and Stong. Controlled surgery is used to reduce topological triviality of core s-cobordisms to a question about controlled homotopy equivalence of 4-manifolds. There are speculations about further reductions. The decompositions on the ends of the s-cobordism are “dual decompositions” with homotopically-controlled handle structures, and the main result is an application of earlier papers in the series.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a49b064d696131ba3df94617b2594bf1 https://doi.org/10.1090/s0002-9947-06-03917-1 Zobrazit plný text záznamu