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/