A sharp signature bound for positive four-braids

Peter Feller

doi:10.1093/qmath/hax036

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arXiv · 1508.00418

A sharp signature bound for positive four-braids

Peter Feller

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Abstract

We provide the optimal linear bound for the signature of positive four-braids in terms of the three-genus of their closures. As a consequence, we improve previously known linear bounds for the signature in terms of the first Betti number for all positive braid links. We obtain our results by combining bounds for positive three-braids with Gordon and Litherland's approach to signature via unoriented surfaces and their Goeritz forms. Examples of families of positive four-braids for which the bounds are sharp are provided.

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Peter Feller. 2015-08-03. A sharp signature bound for positive four-braids. https://doi.org/10.1093/qmath/hax036

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