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A sharp signature bound for positive four-braids (2018)

Feller P.

Oxford University Press

In: Quarterly Journal of Mathematics

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Publication Date: 2018-03-06

Description: 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.

Print ISSN: 0033-5606

Electronic ISSN: 1464-3847

Topics: Mathematics

Published by Oxford University Press

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