|
|||||
|
|
|
|
|
|
|
|
|
Nonorientable surfaces in
homology cobordisms
Adam Simon Levine, Daniel Ruberman and Sašo StrleAppendix: Ira M Gessel |
|
Geometry & Topology 19 (2015) 439–494
|
Abstract |
|
We investigate constraints on embeddings of a nonorientable surface in a –manifold with the homology of , where is a rational homology –sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsváth–Szabó –invariants or Atiyah–Singer –invariants of . One consequence is that the minimal genus of a smoothly embedded surface in is the same as the minimal genus of a surface in . We also consider embeddings of nonorientable surfaces in closed –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 |
|
|
