A Topological Splitting Theorem for Poincare Duality Groups and
  High-dimensional Manifolds

Kar, A; Niblo, GA

Abstract:

We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus theorem, is derived using Cappell's surgery methods from a new algebraic splitting theorem for Poincare duality groups. As an application we derive a new obstruction to the existence of \pi_1-injective maps.

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APA Style

Kar, A., & Niblo, G. A. (2011). A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds.

MLA Style

Kar, A., and G. A. Niblo. A Topological Splitting Theorem for Poincare Duality Groups And High-Dimensional Manifolds. 2011.

Chicago Style

Kar, A, and GA Niblo. 2011. “A Topological Splitting Theorem for Poincare Duality Groups And High-Dimensional Manifolds.”
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+ Kar, A More by this author

Institution:

University of Oxford

Department:

Oxford, MPLS, Mathematical Inst

Role:

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+ Niblo, GA More by this author

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Author

Bibliographic Details

Publication date:: 2011-10-10
URN:: uuid:3629b7e4-14f1-4914-9b2f-f8820efe4eb2
Source identifiers:: 189157
Local pid:: pubs:189157

Item Description

Keywords:: math.GR

Terms of use

Notes:: This is the final version of our article `Topological Superrigidity'

License:: Terms and Conditions of Use for Oxford University Research Archive

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