Embeddings of open manifolds

Cardim, Nancy de Souza

doi:10.1090/s0002-9947-99-02430-7

Trans. Amer. Math. Soc.

1999

DOI: 10.1090/s0002-9947-99-02430-7

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Embeddings of open manifolds

Nancy de Souza Cardim

Abstract: Abstract. Let T OP (M) be the simplicial group of homeomorphisms of M . The following theorems are proved.Theorem A. Let M be a topological manifold of dim ≥ 5 with a finite number of tame ends

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Automorphisms of manifolds

Weiss¹,

Williams²

2001

Princeton University Press eBook Package 2014

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This survey is about homotopy types of spaces of automorphisms of topological and smooth manifolds. Most of the results available are relative, i.e., they compare different types of automorphisms.In chapter 1, which motivates the later chapters, we introduce our favorite types of manifold automorphisms and make a comparison by (mostly elementary) geometric methods. Chapters 2, 3, and 4 describe algebraic models (involving L-theory and/or algebraic K-theory) for certain spaces of "structures" associated with a manifold M , that is, spaces of other manifolds sharing some geometric features with M . The algebraic models rely heavily onWall's work in surgery theory, e.g. [Wa1] , • Waldhausen's work in h-cobordism theory alias concordance theory, which includes a parametrized version of Wall's theory of the finiteness obstruction, [Wa2] .The structure spaces are of interest for the following reason. Suppose that two different notions of automorphism of M are being compared. Let X 1 (M ) and X 2 (M ) be the corresponding automorphism spaces; suppose that X 1 (M ) ⊂ X 2 (M ). As a rule, the space of cosets X 2 (M )/X 1 (M ) is a union of connected components of a suitable structure space.Chapter 5 contains the beginnings of a more radical approach in which one tries to calculate the classifying space BX 1 (M ) in terms of BX 2 (M ), rather than trying to calculate X 2 (M )/X 1 (M ). Chapter 6 contains some examples and calculations.

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Automorphisms of manifolds

Weiss¹,

Williams²

2001

Princeton University Press eBook Package 2014

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show abstract

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Embeddings of open manifolds

Abstract: Abstract. Let T OP (M) be the simplicial group of homeomorphisms of M . The following theorems are proved.Theorem A. Let M be a topological manifold of dim ≥ 5 with a finite number of tame ends

Cited by 1 publication

References 34 publications

Automorphisms of manifolds

Automorphisms of manifolds

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