Homotopy groups of certain highly connected manifolds via loop space homology

Samik Basu; Somnath Basu

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arXiv · 1601.04413

Homotopy groups of certain highly connected manifolds via loop space homology

Samik Basu·Somnath Basu

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Abstract

For $n\geq 2$ we consider $(n-1)$-connected closed manifolds of dimension at most $(3n-2)$. We prove that away from a finite set of primes, the $p$-local homotopy groups of $M$ are determined by the dimension of the space of indecomposable elements in the cohomology ring $H^\ast(M)$. Moreover, we show that these $p$-local homotopy groups can be expressed as direct sum of $p$-local homotopy groups of spheres. This generalizes some of the results of our earlier work.

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BibTeX RIS

Samik Basu, Somnath Basu. 2016-01-18. Homotopy groups of certain highly connected manifolds via loop space homology. https://arxiv.org/abs/1601.04413

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