Event

Luis Garcia - University of Toronto

Thursday, January 10, 2019 16:00to17:00
Burnside Hall Room 1104, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

 

Title: Transgression of the Euler class and arithmetic applications

 

Abstract: I will survey recent work (joint with N. Bergeron and P. Charollois) giving a new construction of certain cohomology classes of SL_N(\bbZ) that were first defined by Nori and Szcech. To motivate our approach, I will start by discussing the problem of how to compute linking numbers in certain three-manifolds that fiber over the circle, e.g in the complement of the trefoil knot in the 3-sphere. We will see that these linking numbers are special values of L-functions, which implies that the latter are rational numbers. Then I will explain some generalizations that relate the topology of real locally symmetric spaces with the arithmetic world of modular forms.

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