**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

Auth: haotianw@como.maths.usyd.edu.au

### 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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