Abstract
Motivation One of the most convenient computational tools for the mod p homology of loop spaces is the cobar-type Eilenberg-Moore spectral sequence (EMSS, for short). The computation of H,(P’C”X; F,) using the path loop fibration nnznx -+ pn”-‘x:“x + R”_‘Z”_X (1) illustrates the power of EMSS. In this case, the spectral sequence E2 = CotorH*(R’~‘r”x;F,)(Fp, F,) =sH,(QTX; F,) collapses at E2, reducing the calculation to an easy homological algebra. On the other hand, the Serre spectral sequence for the fibration (1) contains infinitely many nontrivial differentials and does not compute H,(Q”C”X; F,) directly. It would be very useful to have an EMSS for any generalized homology theory, for example, Morava K-theory.
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