Homology 3-spheres bounding acyclic 4-manifolds

Let $\Sigma(a_1,a_2,\ldots,a_n)$ be a Seifert fibered homology $3$-sphere with $a_1$ even. We show that if $\mu(\Sigma(a_1,a_2,\ldots,a_n))=1 \bmod 2$, then the class of $\Sigma(a_1,a_2,\ldots,a_n)$ has infinite order in the homology cobordism group of homology $3$-spheres. In the proof we use Seiberg-Witten’s monopole equation on four-dimensional V-manifolds.

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Published 1 January 2000