English

Triangulations of Grassmannians and flag manifolds

Combinatorics 2022-10-11 v2

Abstract

MacPherson conjectured that the Grassmannian Gr(2,Rn)\mathrm{Gr}(2, \mathbb{R}^n) has the same homeomorphism type as the combinatorial Grassmannian \mboxMacP(2,n)\|\mbox{MacP}(2,n)\|, while Babson proved that the spaces Gr(2,Rn)\mathrm{Gr}(2,\mathbb{R}^n) and Gr(1,2,Rn)\mathrm{Gr}(1,2,\mathbb{R}^n) are homotopy equivalent to their combinatorial analogs MacP(2,n)\|\mathrm{MacP}(2,n)\| and \mboxMacP(1,2,n)\|\mbox{MacP}(1,2,n)\| respectively. We will prove that Gr(2,Rn)\mathrm{Gr}(2, \mathbb{R}^n) and Gr(1,2,Rn)\mathrm{Gr}(1,2, \mathbb{R}^n) are homeomorphic to \mboxMacP(2,n)\|\mbox{MacP}(2,n)\| and \mboxMacP(1,2,n)\|\mbox{MacP}(1,2,n)\| respectively.

Keywords

Cite

@article{arxiv.2205.09553,
  title  = {Triangulations of Grassmannians and flag manifolds},
  author = {Olakunle S Abawonse},
  journal= {arXiv preprint arXiv:2205.09553},
  year   = {2022}
}

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29 pages