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April 2019 Homotopy groups of certain highly connected manifolds via loop space homology
Samik Basu, Somnath Basu
Osaka J. Math. 56(2): 417-430 (April 2019).

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 $H^\ast(M; \mathbb{Q})$. 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].

Citation

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Samik Basu. Somnath Basu. "Homotopy groups of certain highly connected manifolds via loop space homology." Osaka J. Math. 56 (2) 417 - 430, April 2019.

Information

Published: April 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07080091
MathSciNet: MR3934982

Subjects:
Primary: 55P35, 55Q52
Secondary: 16S37, 57N15

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 2 • April 2019
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