The topological obstructions to the existence of an irreducible SO(3) structure on a five manifold
Marcin Bobienski
TL;DR
This paper investigates the topological conditions necessary for a five-dimensional manifold to admit an irreducible SO(3) structure, focusing on obstructions related to the manifold's topology.
Contribution
It provides necessary and sufficient topological conditions for the existence of an irreducible SO(3) structure on 5-manifolds, expanding understanding of geometric structures on manifolds.
Findings
Identifies topological obstructions to SO(3) structures
Formulates necessary and sufficient conditions for existence
Analyzes the role of the irreducible representation in topology
Abstract
A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation \rho_5 of SO(3) in R^5 is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are investigated. The necessary and sufficient conditions are formulated.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology