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 …
Computing (co)homology can be rather hard without the appropriate tools. The Serre spectral sequence is one such tool. We compute the important example of , and also provide a different proof of Proposition 3.22 in Hatcher’s Algebraic Topology, namely the computation of , where is the reduced James product (see section 4.J, for James). (Note […]
