On the non-existence of certain branched covers

Pekka Pankka; Juan Souto

On the non-existence of certain branched covers

Geometric Topology 2010-08-11 v1 Algebraic Topology Complex Variables

Authors: Pekka Pankka , Juan Souto

Abstract

We prove that while there are maps $\bT^4\to\#^3(\bS^2\times\bS^2)$ of arbitrarily large degree, there is no branched cover from $4$ -torus to $\#^3(\bS^2\times \bS^2)$ . More generally, we obtain that, as long as $N$ satisfies a suitable cohomological condition, any $\pi_1$ -surjective branched cover $\bT^n \to N$ is a homeomorphism.

Keywords

branched covers 4-torus cohomological condition pi_1-surjective homeomorphism degree

Cite

@article{arxiv.1008.1694,
  title  = {On the non-existence of certain branched covers},
  author = {Pekka Pankka and Juan Souto},
  journal= {arXiv preprint arXiv:1008.1694},
  year   = {2010}
}

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