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A
topological splitting theorem for Poincaré duality groups and
high-dimensional manifolds
Aditi Kar and Graham A Niblo |
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Geometry & Topology 17 (2013) 2203–2221
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Abstract |
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We show that for a wide class of manifold pairs with , every –injective map 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 Poincaré duality groups. As an application we derive a new obstruction to the existence of –injective maps. |
Keywords
Torus theorem, Poincaré duality group, Bass–Serre theory,
Kazhdan's property (T), Borel conjecture, surgery,
Cappell's splitting theorem, embeddings, rigidity,
geometric group theory, quaternionic hyperbolic manifolds
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Mathematical Subject Classification 2000
Primary: 20F65, 57N35
Secondary: 57R67, 57Q20, 57P10
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References |
Publication
Received: 10 October 2011
Revised: 19 October 2011
Accepted: 25 April 2013
Published: 26 July 2013
Proposed: Martin R Bridson
Seconded: Walter Neumann, Benson Farb
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Authors |
| Aditi Kar | |
| Mathematical Institute University of Oxford 24–29 St Giles’ Oxford OX1 3LB UK |
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| http://people.maths.ox.ac.uk/kar/ | |
| Graham A Niblo | |
| Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ UK |
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| http://www.personal.soton.ac.uk/gan/ | |
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