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Universal realisators for
homology classes
Alexander Gaifullin |
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Geometry & Topology 17 (2013) 1745–1772
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Abstract |
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We study oriented closed manifolds possessing the following universal realisation of cycles (URC) property: For each topological space and each homology class , there exists a finite-sheeted covering and a continuous mapping such that for a non-zero integer . We find a wide class of examples of such manifolds among so-called small covers of simple polytopes. In particular, we find 4–dimensional hyperbolic manifolds possessing the URC property. As a consequence, we obtain that for each 4–dimensional oriented closed manifold , there exists a mapping of non-zero degree of a hyperbolic manifold to . This was earlier conjectured by Kotschick and Löh. |
Keywords
realisation of cycles, hyperbolic manifold, simple
polytope, small cover, permutahedron, Coxeter group,
negative curvature
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Mathematical Subject Classification 2010
Primary: 57N65
Secondary: 53C23, 52B70, 20F55
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References |
Publication
Received: 7 April 2012
Accepted: 4 March 2013
Published: 30 June 2013
Proposed: David Gabai
Seconded: Benson Farb, Ronald Stern
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Authors |
| Alexander Gaifullin | ||
| Department of Geometry and
Topology Steklov Mathematical Institute 8 Gubkina Str Moscow 119991 Russia |
Lomonosov Moscow State
University Leninskie Gory Moscow 119991 Russia |
Institute for Information
Transmission Problems (Kharkevich Institute) 19 Bolshoy Karetny per Moscow 127994 Russia |
| http://www.iitp.ru/en/users/919.htm | ||
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