Virtual homology of surgered torus bundles

Details Virtual homology of surgered torus bundles Virtual homology of surgered torus bundles

1998-12-11

arxiv.org/abs/math/9812068v1

Mathematics

Geometric Topology

19 pages, 9 figures

Scientific paper

Let $M$ be a once-punctured torus bundle over $S^1$ with monodromy $h$.
We show that, under certain hypotheses on $h$, "most" Dehn-fillings of $M$ (in
some cases all but finitely many) are virtually
$\mathbb{Z}$-representable. We apply our results to show that surgeries on the
figure-eight knot with even numerator are virtually $\mathbb{Z}$-representable.

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