On classical upper bounds for slice genera

Feller, Peter; Lewark, Lukas Pascal (2018). On classical upper bounds for slice genera. Selecta mathematica, 24(5), pp. 4885-4916. Springer 10.1007/s00029-018-0435-x

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We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the minimal genus of a surface in the four-ball whose complement has infinite cyclic fundamental group. We characterize the algebraic genus in terms of cobordisms in three-space, and explore the connections to other knot invariants related to the Seifert form, the Blanchfield form, knot genera and unknotting. Employing Casson-Gordon invariants, we discuss the algebraic genus as a candidate for the optimal upper bound for the topological slice genus that is determined by the S-equivalence class of Seifert matrices.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Feller, Peter and Lewark, Lukas Pascal

Subjects:

500 Science > 510 Mathematics

ISSN:

1022-1824

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

14 May 2019 15:50

Last Modified:

23 Oct 2019 14:05

Publisher DOI:

10.1007/s00029-018-0435-x

BORIS DOI:

10.7892/boris.125475

URI:

https://boris.unibe.ch/id/eprint/125475

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