Embedding Heegaard Decompositions

2019/06/07 by Agol, Ian, Freedman, Michael H.
#57M #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1906.03244

Abstract

A smooth embedding of a closed 3-manifold M in ℝ⁴ may generically be composed with projection to the fourth coordinate to determine a Morse function on M and hence a Heegaard splitting M=X∪_ΣY. However, starting with a Heegaard splitting, we find an obstruction coming from the geometry of the curve complex C(Σ) to realizing a corresponding embedding M\hookrightarrow ℝ⁴.

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