Vol. 315, No. 1, 2021

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Ribbon cobordisms between lens spaces

Marius Huber

Vol. 315 (2021), No. 1, 111–128
Abstract

We determine when there exists a ribbon rational homology cobordism between two connected sums of lens spaces, i.e., one without 3-handles. In particular, we show that if an oriented rational homology sphere Y admits a ribbon rational homology cobordism to a lens space, then Y must be homeomorphic to L(n,1), up to orientation-reversal. As an application, we classify ribbon χ-concordances between connected sums of 2-bridge links. Our work builds on Lisca’s work on embeddings of linear lattices.

Keywords
lens space, ribbon cobordism, intersection lattice, 2-bridge knot
Mathematical Subject Classification
Primary: 57M99
Milestones
Received: 6 April 2021
Revised: 16 September 2021
Accepted: 17 September 2021
Published: 13 December 2021
Authors
Marius Huber
Department of Mathematics
Boston College
Chestnut Hill, MA
United States