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

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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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publication date:
2011-10-10
URN:
uuid:3629b7e4-14f1-4914-9b2f-f8820efe4eb2
Source identifiers:
189157
Local pid:
pubs:189157
Keywords:

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