Algebra/Topology Seminar

Speaker: Kaif Hilman

Title: Quinn’s bordism-type spectra revisited

Abstract: In his seminal thesis and its follow-up, Quinn introduced the perspective of “bordism-type spectra” as a template for cobordism spectra and L-theory. In order to incorporate multiplicative structures into this, Laures and McClure subsequently set up the framework of “ad-theories” using semisimplicial sets. Unfortunately, it is rather difficult to connect this to the more recent approaches to hermitian K-theory.

In this talk, I will propose a new formalism to achieve this, which, as a byproduct, gives a new construction of the lax symmetric monoidal structure on algebraic K-theory. This reports on joint work-in-progress with Andrea Bianchi, Dominik Kirstein, and Christian Kremer; all of this is part of an ongoing project on the index and signature maps on cobordisms joint additionally with Fabian Hebestreit, Markus Land, Thomas Nikolaus, and Wolfgang Steimle.