Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Heegaard Splittings of Three Manifolds and the Reidemeister-Singer theorem

Student-Run Applied & Math Seminar

Speaker: Dale Koenig, UC Davis
Location: 2112 MSB
Start time: Wed, Feb 10 2016, 12:10PM

Every compact orientable 3-manifold can be broken into two simple pieces, called a Heegaard splitting. There is a notion of stabilization on these splittings, and in fact any two such splittings are identical after enough stabilizations. This is called the Reidemeister-Singer theorem. I will describe Heegaard splittings and prove that they always exist. I will give some simple examples of the decompositions. If there is time, I will provide some intuition as to why a 3-manifold can have multiple Heegaard splittings of a given complexity.