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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 …
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 …