21-23 October 2015
Institut de Mathématiques de Toulouse
Europe/Paris timezone
21-23 Octobre 2015, Institut de Mathématiques de Toulouse

The rational classification of (n-1)-connected (4n-1)-manifolds (n > 1)

21 Oct 2015, 14:20
50m
Amphi Schwartz, bat. 1R3 (Institut de Mathématiques de Toulouse)

Amphi Schwartz, bat. 1R3

Institut de Mathématiques de Toulouse

118 Route de Narbonne 31068 Toulouse
Exposé de recherche sur invitation TopAlg

Speaker

Dr Diarmuid Crowley (Aberdeen)

Description

I shall report on joint work with Johannes Nordström in which we identify a new invariant of the rational homotopy type of a space X, which we call the Bianchi-Massey tensor. The Bianchi-Massey tensor is a linear map on the degree (4n-1) rational cohomology of X taking values in a subspace of the 4-fold tensor product of the degree n cohomology of X. We use the Bianchi-Massey tensor to show that there are many (n-1)-connected (4n-1)-manifolds which are not formal but which have no non-zero Massey products, and to present a classification of simply-connected 7-manifolds up to finite ambiguity.

Primary author

Dr Diarmuid Crowley (Aberdeen)

Presentation Materials

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