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On the nonexistence of certain branched covers

Pekka Pankka and Juan Souto

Geometry & Topology 16 (2012) 1321–1344

DOI: 10.2140/gt.2012.16.1321
Abstract

We prove that while there are maps T4 → #3(S2 × S2) of arbitrarily large degree, there is no branched cover from the 4–torus to #3(S2 × S2). More generally, we obtain that, as long as a closed manifold N satisfies a suitable cohomological condition, any π1–surjective branched cover Tn → N is a homeomorphism.

Keywords

branched cover, quasiregularly elliptic manifold
Mathematical Subject Classification

Primary: 57M12

Secondary: 30C65, 57R19
References
Publication

Received: 25 January 2011
Revised: 27 January 2012
Accepted: 2 February 2012
Published: 10 July 2012
Proposed: David Gabai
Seconded: Benson Farb, Ronald Fintushel
Authors
Pekka Pankka
Department of Mathematics and Statistics
University of Helsinki
PO Box 68 (Gustaf Hällströmin katu 2b)
FI-00014 Helsinki
Finland
www.helsinki.fi/~pankka
Juan Souto
Mathematics Department
University of British Columbia
1984 Mathematics Road
Vancouver BC V6T 1Z2
Canada
http://www.math.ubc.ca/~jsouto