SMS scnews item created by Zhou Zhang at Thu 6 Jun 2013 1208
Type: Seminar
Distribution: World
Expiry: 27 Jun 2013
Calendar1: 11 Jun 2013 1200-1300
CalLoc1: AGR Carslaw 829
Auth: zhangou@como.maths.usyd.edu.au

# GTA Seminar: Johnson -- The Structure of High Distance Heegaard Splittings

Speaker: Dr. Jesse Johnson (Oklahoma State University)

http://www.math.okstate.edu/~jjohnson/

Time: **Tuesday**, June 11, 12NOON--1PM

Room: AGR, Carslaw 829

Lunch: after the talk.

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Title: The Structure of High Distance Heegaard Splittings

Abstract: A Heegaard splitting is a decomposition of a
three-dimensional manifold into two simple pieces called
handlebodies, glued along an embedded surface. The notion
of distance for a Heegaard splitting of a three-dimensional
manifold $M$, introduced by John Hempel, has proved to be
a very powerful tool for understanding the geometry and
topology of $M$. I will describe how distance, and a
slight generalization known as subsurface projection
distance, can be used to explore the connection between
geometry and topology at the center of the modern theory
hyperbolic three-manifolds.

In particular, Schalremann-Tomova showed that if a Heegaard
splitting for $M$ has high distance then it will be the only
irreducible Heegaard splitting of $M$ with genus less than
a certain bound. I will explain this result in terms of both
a geometric proof and a topological proof. Then, using the
notion of subsurface distance, I will describe a construction
of a manifold with multiple distinct low-distance Heegaard
splittings of the same (small) genus, and a manifold with
both a high distance, low-genus Heegaard splitting and a
distinct, irreducible high-genus, low-distance Heegaard
splitting.

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/

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