Embeddings of non-orientable surfaces in orientable manifolds

Saso Strle (Univerza v Ljubljani)

Monday 10th February, 2014 16:00-17:00 Maths 204


A closed non-orientable surface admits an embedding in any orientable 4-dimensional manifold but in general not in an orientable 3-manifold. In the latter case the obstruction is homological in nature. After reviewing some classical results I will discuss recent joint work with Adam Levine and Daniel Ruberman on non-trivial embeddings in 4-dimensional homology cobordisms. Based on Heegaard Floer homology correction terms we find obstructions to such embeddings involving the genus of the surface and the normal Euler number of the embedding. For embeddings in a lens space times an interval these numbers are the same as those obtained by stabilization of embeddings in the lens space.

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