# Mathematics Colloquia and Seminars

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### STABILIZED CHARACTER VARIETIES FOR SURFACES AND THE CHERN-SIMONS LINE BUNDLE

**Geometry/Topology**

Speaker: | Dan Ramras,, Mathematics Department, IUPUI |

Location: | |

Start time: | Thu, Mar 12 2015, 3:10PM |

For a surface group Γ = π1(Mg), the character variety, Hom(Γ, SU(n))/SU(n), carries a natural symplectic structure on its (Zariski) tangent spaces. Ramadas, Singer, and Weitsman showed that this structure arises from a line bundle with connection, defined in terms of the Chern-Simons functional. The colimit of these moduli spaces as n tends to infinity can be studied using a combination of K-theoretic methods and covering space theory. This leads to a computation of its homotopy groups, showing that it is a K(Z, 2) space. In fact, we show that the classifying map for the Chern-Simon line bundle induces a homotopy equivalence (in the large n limit) with CP∞. This is joint work with S. Lawton and also with L. Jeffrey and J. Weitsman.