Algebraic models for topological spaces
Speaker:Prof. Dr. Birgit Richter, Universität Hamburg
Location:Mathematisches Institut, Bunsenstr 3-5Sitzungszimmer oder Zoom: https://uni-goettingen.zoom.us/j/91336854872
Classically, there are several algebraic models for rational topological spaces, ranging from differential graded commutative algebras, Lie algebras to cocommutative coalgebras. In joint work with Steffen Sagave we find a strictly commutative model for the cochain algebra of a space over an arbitrary ground ring. This model is built in the category of $I$-chain complexes, where $I$ is the category of finite sets and injections. In this talk we review this result and explain how it determines the integral homotopy type of (nilpotent) spaces (of finite type). I will also describe features of the category of $I$-chain complexes and discuss how these might affect the chances of finding algebraic models for spaces via comonoids in $I$-chain complexes.
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Direct link to event:https://events.goettingen-campus.de/event?eventId=29148