Volume 19, issue 1 (2015)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Nonorientable surfaces in homology cobordisms

Adam Simon Levine, Daniel Ruberman and Sašo Strle

Appendix: Ira M Gessel

Geometry & Topology 19 (2015) 439–494
Abstract

We investigate constraints on embeddings of a nonorientable surface in a 4–manifold with the homology of M × I, where M is a rational homology 3–sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsváth–Szabó d–invariants or Atiyah–Singer ρ–invariants of M. One consequence is that the minimal genus of a smoothly embedded surface in L(2k,q) × I is the same as the minimal genus of a surface in L(2k,q). We also consider embeddings of nonorientable surfaces in closed 4–manifolds.

Keywords
nonorientable surfaces, $4$–manifold, Heegaard Floer homology, Dedekind sums
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R40, 57R58
References
Publication
Received: 9 November 2013
Accepted: 25 May 2014
Published: 27 February 2015
Proposed: Cameron Gordon
Seconded: Ciprian Manolescu, Peter Teichner
Authors
Adam Simon Levine
Department of Mathematics
Princeton University
Fine Hall, Washington Road
Princeton, NJ 08540
USA
Daniel Ruberman
Department of Mathematics
Brandeis University
MS 050
Waltham, MA 02454
USA
Sašo Strle
Faculty of Mathematics and Physics
University of Ljubljana
Jadranska 21
1000 Ljubljana
Slovenia
Ira M Gessel
Department of Mathematics
Brandeis University
MS 050
415 South Street
Waltham, MA 02454
USA