Geometry & Topology

Nonorientable surfaces in homology cobordisms

Adam Levine, Daniel Ruberman, and Sašo Strle

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57R40: Embeddings 57R58: Floer homology

nonorientable surfaces $4$–manifold Heegaard Floer homology Dedekind sums


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.

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