The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3

Diarmuid Crowley; Johannes Nordström

doi:10.1112/topo.12133

The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3

Diarmuid Crowley, Johannes Nordström

Department of Mathematical Sciences

University of Melbourne

Research output: Contribution to journal › Article › peer-review

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Abstract

We define the Bianchi–Massey tensor of a topological space (Formula presented.) to be a linear map (Formula presented.), where (Formula presented.) is a subquotient of (Formula presented.) determined by the algebra (Formula presented.). We then prove that if (Formula presented.) is a closed (Formula presented.) -connected manifold of dimension at most (Formula presented.) (and (Formula presented.)) then its rational homotopy type is determined by its cohomology algebra and Bianchi–Massey tensor, and that (Formula presented.) is formal if and only if the Bianchi–Massey tensor vanishes. We use the Bianchi–Massey tensor to show that there are many (Formula presented.) -connected (Formula presented.) -manifolds that are not formal but have no non-zero Massey products, and to present a classification of simply connected 7-manifolds up to finite ambiguity.

Original language	English
Pages (from-to)	539-575
Number of pages	37
Journal	Journal of Topology
Volume	13
Issue number	2
Early online date	18 Mar 2020
DOIs	https://doi.org/10.1112/topo.12133
Publication status	Published - 1 Jun 2020

Keywords

55P62
57R19 (primary)

ASJC Scopus subject areas

Geometry and Topology

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10.1112/topo.12133

1505.04184v3.pdf
This is the peer reviewed version of the following article: Crowley, D. and Nordström, J. (2020), The rational homotopy type of ( n − 1 ) ‐connected manifolds of dimension up to 5 n − 3 . Journal of Topology, 13: 539-575. , which has been published in final form at https://doi.org/10.1112/topo.12133. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Accepted author manuscript, 491 KB

https://arxiv.org/abs/1505.04184v3Licence: Unspecified

Cite this

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The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3

Abstract

Keywords

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