2023/01/24 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2301.09827
We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology algebra of the classifying space of a topological category. By applying the machinery to a Borel construction, we determine explicitly the mod p cohomology algebra of the free loop space of the real projective space for each odd prime p. This is highlighted as an important computational example of such a spectral sequence. Moreover, we try to represent generators in the singular de Rham cohomology algebra of the diffeological free loop space of a non-simply connected manifold M with differential forms on the universal cover of M via Chen's iterated integral map.