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From SFB1085 - Higher Invariants
Jump to navigationJump to searchAbstract: Based on joint work-in-progress with Bianchi, Kirstein, and Kremer, I will introduce a proposed notion of categorical symmetric spectra as well as an enlargement of the category of Poincare categories which we call that of bundled categories. As applications, we construct the commutative ring cobordism spectrum of Poincare spaces equipped with Pontryagin-Thom maps, and give a new proof that K-theory is lax symmetric monoidal. Time permitting, I will also discuss further joint work additionally with Hebestreit, Land, Nikolaus, and Steimle on using this setup to construct the Weiss-Williams index and signature maps.