Orientability of vector bundles over real flag manifolds
Mauro Patr\~ao, Luiz A. B. San Martin, La\'ercio J. dos Santos, Lucas, Seco
TL;DR
This paper studies the orientability of vector bundles over real flag manifolds, providing explicit formulas based on roots for bundles like tangent and stable bundles of gradient flows.
Contribution
It offers new closed-form formulas, in terms of roots, to determine the orientability of various vector bundles over real flag manifolds.
Findings
Closed formulas for orientability based on roots.
Applicability to tangent and stable bundles of gradient flows.
Enhanced understanding of bundle properties over real flag manifolds.
Abstract
We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are provided.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Advanced Algebra and Geometry