The totally nonnegative part of G/P is a CW complex
Konstanze Rietsch, Lauren Williams
TL;DR
This paper proves that the totally nonnegative part of a partial flag variety G/P has a CW complex structure by constructing explicit glueing maps, generalizing previous results for Grassmannians.
Contribution
It introduces explicit glueing maps for cells in the totally nonnegative part of G/P, establishing its CW complex structure.
Findings
The totally nonnegative part of G/P is a CW complex.
The closure of each cell is a union of smaller cells.
Generalizes previous Grassmannian results.
Abstract
The totally nonnegative part of a partial flag variety G/P has been shown by the first author to be a union of semi-algebraic cells. Moreover she showed that the closure of a cell is the union of smaller cells. In this note we provide glueing maps for each of the cells to prove that the totally nonnegative part of G/P is a CW complex. This generalizes a result of Postnikov, Speyer and the second author for Grassmannians.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology