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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

6 votes

What is known about K-theory and K-homology groups of (free) loop spaces?

I take the liberty to reference to a paper of mine (which is hopefully no bad style): Spectral Sequences in String Topology. Here, the K-homology of the free loop spaces of spheres and complex project …
Lennart Meier's user avatar
7 votes

Finiteness of stable homotopy groups of spheres

Let me phrase a proof of Serre's computation of the rational stable homotopy groups of spheres as stably as I can: For every spectrum $X$, we can define its rationalization $X_{\mathbb{Q}}$ as the ho …
Lennart Meier's user avatar