Topology, Algebraic Geometry, and Dynamics Seminar (TADS): Higher scissors congruence invariants for manifolds

Speaker:  Mona Merling, University of Pennsylvania

Title:  Higher scissors congruence invariants for manifolds

Abstract:  The classical scissors congruence problem asks whether given two polyhedra with the same volume, one can cut one into a finite number of smaller polyhedra and reassemble these to form the other. There is an analogous definition of an SK (German "schneiden und kleben," cut and paste) relation for manifolds and classically defined scissors congruence (SK) groups for manifolds. Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic K-theory, and applying these tools to studying the Grothendieck ring of varieties. I will talk about a new application of this framework: we will construct a K-theory spectrum of manifolds, which lifts the classical SK group, and a derived version of the Euler characteristic. I will discuss what this higher homotopical lift of the Euler characteristic sees on the level of pi_1.

Time:  Friday, November 10, 1:30pm – 2:30pm

Place:  Exploratory Hall, room L111