SMS scnews item created by Haotian Wu at Wed 14 Mar 2018 1240
Type: Seminar
Distribution: World
Expiry: 13 Jun 2018
Calendar1: 15 Mar 2018 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry & Topology Seminar: Tillmann -- Computing trisections of 4-manifolds

Geometry & Topology Seminar

Computing trisections of 4-manifolds

Stephan Tillmann (Sydney)

Thursday 15 March 12:00–13:00 in Carslaw 535A.

Please join us for lunch after the talk.

Abstract: 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. The minimal genus of such a surface is the trisection genus of the 4-manifold.

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. I will also describe joint work with Jonathan Spreer that determines the trisection genus for each of the standard simply connected PL 4-manifolds.

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