The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

On functorial decompositions of self-smash products

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Functorial decompositions of looped coassociative co-H spaces

Canadian Journal of Mathematics584877-89

Functorial homotopy decompositions of looped co-H spaces

In recent work of the first and third authors, functorial coalgebra decompositions of tensor algebras were geometrically realized to give functorial homotopy decompositions of loop suspensions. Later work by all three authors generalized this to functorial decompositions of looped coassociative co-H spaces. In this paper we use different methods which allow for the coassociative hypothesis to be removed

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10.1016/j.jpaa.2008.04.011Journal of Pure and Applied Algebra212112570-2580JPAA

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