nLab homology of loop spaces




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 analogous construction over compact Lie groups in:

  • Lev Pontrjagin, Homologies in compact Lie groups, Rec. Math. [Mat. Sbornik] N.S., 1939 Volume 6(48), Number 3, Pages 389–422 (mathnet:5835)

Further discussion of homology of (iterated) loop spaces:

See also:

Last revised on January 21, 2024 at 12:43:09. See the history of this page for a list of all contributions to it.