Volume 19, issue 4 (2015)

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Virtual domination of $3$–manifolds

Hongbin Sun

Geometry & Topology 19 (2015) 2277–2328
Abstract

For any closed oriented hyperbolic $\mathfrak{3}$–manifold $M$ and any closed oriented $\mathfrak{3}$–manifold $N$, we show that $M$ admits a finite cover ${M}^{\prime }$ such that there exists a degree-$\mathfrak{2}$ map $f:{M}^{\prime }\to N$, ie $M$ virtually $\mathfrak{2}$–dominates $N$.

Keywords
hyperbolic $3$–manifold, finite cover, degree-nonzero map
Mathematical Subject Classification 2010
Primary: 57M10
Secondary: 30F40, 57M50