Making lifting obstructions explicit

Neeb KH, Wagemann F, Wockel C (2013)

Publication Type: Journal article, Original article

Publication year: 2013

Journal

Proceedings of the London Mathematical Society London Mathematical Society

Publisher: London Mathematical Society

Book Volume: 106

Pages Range: 589 - 620

Journal Issue: 3

DOI: 10.1112/plms/pds047

Abstract

If P→X is a topological principal K-bundle and Graphic a central extension of K by Z, then there is a natural obstruction class Graphic in sheaf cohomology whose vanishing is equivalent to the existence of a Graphic-bundle Graphic over X with Graphic. In this paper, we establish a link between homotopy theoretic data and the obstruction class δ1(P) which in many cases can be used to calculate this class in explicit terms. Writing Graphic for the connecting maps in the long exact homotopy sequence, two of our main results can be formulated as follows. If Z is a quotient of a contractible group by the discrete group Γ, then the homomorphism π3(X)→Γ induced by Graphic coincides with Graphic and if Z is discrete, then Graphic induces the homomorphism Graphic. We also obtain some information on obstruction classes defining trivial homomorphisms on homotopy groups

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

How to cite

APA:

Neeb, K.H., Wagemann, F., & Wockel, C. (2013). Making lifting obstructions explicit. Proceedings of the London Mathematical Society, 106(3), 589 - 620. https://doi.org/10.1112/plms/pds047

MLA:

Neeb, Karl Hermann, Friedrich Wagemann, and Christoph Wockel. "Making lifting obstructions explicit." Proceedings of the London Mathematical Society 106.3 (2013): 589 - 620.

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