Computing trisections of 4–manifolds

Stephan Tillmann
University of Sydney

Date(s) : 04/09/2017   iCal
14 h 00 min - 15 h 00 min

Gay and Kirby recently generalised Heegaard splittings of 3-manifolds to trisections of 4-manifolds. A trisection describes a 4–dimensional manifold as a union of three 4–dimensional handlebodies. The complexity of the 4–manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies.

After defining trisections and giving key examples and applications, I will describe an algorithm to compute trisections of 4–manifolds using arbitrary triangulations as input. This results in the first explicit complexity bounds for the trisection genus of a 4–manifold in terms of the number of pentachora (4–simplices) in a triangulation.

This is joint work with Mark Bell, Joel Hass and Hyam Rubinstein.


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