Obstruction theory on 8-manifolds

2007/10/03 by Martin Čadek, Martin Cadek, M. C. Crabb +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:55R50 #msc:57N16

paper · pdf · doi:10.1007/s00229-008-0203-x

published as manuscripta math. 127 (2008), 167-186 · 19 pages

arxiv created 2007/10/03 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological critera for the existence of almost complex and almost quaternionic structures on the tangent bundle and for the reduction of the structure group to U(3) by the homomorphism U(3) --> O(8) given by the Lie algebra representation of PU(3).

Citations

• Special metric structures and closed forms

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• New invariants ofG2–structures

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