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Geometry-Topology Seminar

Thursday, March 28, 2019 - 4:30pm

Carmen Rovi

Indiana University


University of Pennsylvania


Abstract: The K-theory K_n(ZG) and quadratic L-theory L_n(ZG) functors provide information about the algebraic and geometric topology of a smooth manifold X with fundamental group G = π1(X, x0).  Both K- and L-theory are difficult to compute in general and assembly maps give important information about these functors.   Ranicki developed a combinatorial version of assembly by describing L-theory over additive bordism categories indexed over simplicial complexes. In this talk, I will present current work with Jim Davis where we define an equivariant version of Ranicki’s local / global assembly map and identify our local / global assembly map with the map on equivariant homology defined by Davis and Lueck.  I will also mention some applications of our results.