Osaka Journal of Mathematics

Homotopy groups of certain highly connected manifolds via loop space homology

Samik Basu and Somnath Basu

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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 $H^\ast(M; \mathbb{Q})$. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. This generalizes some of the results of our earlier work [1].

Article information

Osaka J. Math., Volume 56, Number 2 (2019), 417-430.

First available in Project Euclid: 3 April 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P35: Loop spaces 55Q52: Homotopy groups of special spaces
Secondary: 16S37: Quadratic and Koszul algebras 57N15: Topology of $E^n$ , $n$-manifolds ($4 \less n \less \infty$)


Basu, Samik; Basu, Somnath. Homotopy groups of certain highly connected manifolds via loop space homology. Osaka J. Math. 56 (2019), no. 2, 417--430.

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