Lefschetz fibrations on knot surgery $4$-manifolds via Stallings twist

Jongil Park; Ki-Heon Yun

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arXiv · 1503.06272

Lefschetz fibrations on knot surgery $4$-manifolds via Stallings twist

Jongil Park·Ki-Heon Yun

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Abstract

In this article we construct a family of knot surgery $4$-manifolds admitting arbitrarily many nonisomorphic Lefschetz fibration structures with the same genus fiber. We obtain such families by performing knot surgery on an elliptic surface $E(2)$ using connected sums of fibered knots obtained by Stallings twist from a slice knot $3_1 \sharp 3^*_1$. By comparing their monodromy groups induced from the corresponding monodromy factorizations, we show that they admit mutually nonisomorphic Lefschetz fibration structures.

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BibTeX RIS

Jongil Park, Ki-Heon Yun. 2015-03-21. Lefschetz fibrations on knot surgery $4$-manifolds via Stallings twist. https://arxiv.org/abs/1503.06272

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