A sharp signature bound for positive four-braids
Geometric Topology
2018-06-15 v2
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.
Keywords
Cite
@article{arxiv.1508.00418,
title = {A sharp signature bound for positive four-braids},
author = {Peter Feller},
journal= {arXiv preprint arXiv:1508.00418},
year = {2018}
}
Comments
12 pages, 6 figures, comments welcome! Accepted for publication in Q. J. Math