Geometry & Topology
- Geom. Topol.
- Volume 19, Number 1 (2015), 439-494.
Nonorientable surfaces in homology cobordisms
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.
Geom. Topol., Volume 19, Number 1 (2015), 439-494.
Received: 9 November 2013
Accepted: 25 May 2014
First available in Project Euclid: 16 November 2017
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Levine, Adam; Ruberman, Daniel; Strle, Sašo. Nonorientable surfaces in homology cobordisms. Geom. Topol. 19 (2015), no. 1, 439--494. doi:10.2140/gt.2015.19.439. https://projecteuclid.org/euclid.gt/1510858685