homology of loop spaces
Urs Schreiber
The homology of (iterated) based loop spaces (ordinary homology or generalized homology) carries special structure, reflecting the ∞-group-structure of based loop spaces.
In particular, under mild technical conditions (see Milnor-Moore 65, p. 262, Halperin 92) the Pontrjagin ring-structure induced by concatenation of loops enhances the homology coalgebra induced by the diagonal maps to that of a Hopf algebra.
The “Pontryagin-multiplication” on loop/path spaces is due to
named in honor of the...