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# Adam Levine : Non-orientable surfaces in homology cobordisms

We study the minimal genus problem for embeddings of closed, non-orientable surfaces in a homology cobordism between rational homology spheres, using obstructions derived from Heegaard Floer homology and from the Atiyah-Singer index theorem. For instance, we show that if a non-orientable surface embeds essentially in the product of a lens space with an interval, its genus and normal Euler number are the same as those of a stabilization of a non-orientable surface embedded in the lens space itself. This is joint work with Danny Ruberman and Saso Strle.

**Category**: Geometry and Topology**Duration**: 01:14:49**Date**: October 29, 2013 at 4:25 PM**Views**: 119-
**Tags:**seminar, Geometry/topology Seminar

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