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Torsions of connections on tangent bundles of higher order

Kureš, Miroslav (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

The torsions of a general connection Γ on the r th-order tangent bundle of a manifold M are defined as the Frölicher-Nijenhuis bracket of Γ with the natural affinors. The author deduces the basic properties of these torsions. Then he compares them with the classical torsion of a principal connection on the r th-order frame bundle of M .

Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A fibration F E B is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if H * ( E ; k ) H * ( F ; k ) is surjective. This is equivalent to saying that π 1 ( B ) acts trivially on H * ( F ; k ) and the Serre spectral sequence collapses at E 2 . S. Halperin conjectured that for c h a r ( k ) = 0 and F a 1-connected rationally elliptic space (i.e., both H * ( F ; 𝒬 ) and π * ( F ) 𝒬 are finite dimensional) such that H * ( F ; k ) vanishes in odd degrees, every fibration F E B is TNCZ. The author proves this being the case...

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