Topology of the octonionic flag manifold
Augustin-Liviu Mare, Matthieu Willems

TL;DR
This paper explores the topological and equivariant cohomology and K-theory of the octonionic flag manifold, providing explicit descriptions and new computational tools for these sophisticated geometric structures.
Contribution
It offers Borel type descriptions of cohomology and K-theory for the octonionic flag manifold, including Goresky-Kottwitz-MacPherson type formulas, advancing understanding of its equivariant topology.
Findings
Borel type descriptions of $Spin(8)$-equivariant cohomology
GKM type description of the cohomology ring
GKM type description of the equivariant K-theory ring
Abstract
The octonionic flag manifold is the space of all pairs in (where denotes the octonionic projective plane) which satisfy a certain "incidence" relation. It comes equipped with the projections , which are bundles, as well as with an action of the group . The first two results of this paper give Borel type descriptions of the usual, respectively -equivariant cohomology of in terms of and (actually the Euler classes of the tangent spaces to the fibers of , respectively , which are rank 8 vector bundles on ). Then we obtain a Goresky-Kottwitz-MacPherson type description of the ring . Finally, we consider the -equivariant -theory ring of…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
