Heegaard diagrams for $5$-manifolds

Geunyoung Kim

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arXiv · 2505.06887

Heegaard diagrams for $5$-manifolds

Geunyoung Kim

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Abstract

We introduce a version of Heegaard diagrams for $5$-dimensional cobordisms with $2$- and $3$-handles, $5$-dimensional $3$-handlebodies, and closed $5$-manifolds. We show that every such smooth $5$-manifold can be represented by a Heegaard diagram, and that two Heegaard diagrams represent diffeomorphic $5$-manifolds if and only if they are related by certain moves. As an application, we construct Heegaard diagrams for $5$-dimensional cobordisms from the standard $4$-sphere to the Gluck twists along knotted $2$-spheres. This provides several statements equivalent to the Gluck twist being diffeomorphic to the standard $4$-sphere.

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Geunyoung Kim. 2025-05-11. Heegaard diagrams for $5$-manifolds. https://arxiv.org/abs/2505.06887

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