Renée Hoekzema: Cut and paste invariants of manifolds via algebraic K-theory

Abstract: Cut and paste or SK groups of manifolds are formed by quotienting manifolds by the relation that two manifolds are equivalent if I can cut one up into pieces and glue them back together to form the other manifold. Cobordism cut and paste groups are formed by moreover quotienting by cobordism (smooth evolution over time). We categorify these classical groups to spectra using a new framework for algebraic K-theory, and lift two canonical homomorphisms of groups to maps of spectra. This is joint work with Mona Merling, Laura Murray, Carmen Rovi and Julia Semikina.