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arXiv · 1610.03937

Virtual 1-domination of 3-manifolds

Yi Liu·Hongbin Sun
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Abstract

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that manifold. This improves a known result of virtual 2-domination. The proof invokes a recently developed enhanced version of the connection principle in good pants constructions.

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Yi Liu, Hongbin Sun. 2016-10-13. Virtual 1-domination of 3-manifolds. https://doi.org/10.1112/s0010437x17007965

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