English

Boundary measurement and sign variation in real projective space

Combinatorics 2023-04-28 v2

Abstract

We define two generalizations of the totally nonnegative Grassmannian and determine their topology in the case of real projective space. We find the spaces to be PL manifolds with boundary which are homotopy equivalent to another real projective space of smaller dimension. One generalization makes use of sign variation while the other uses boundary measurement. Spaces arising from boundary measurement are shown to admit Cohen-Macaulay triangulations.

Keywords

Cite

@article{arxiv.1909.04640,
  title  = {Boundary measurement and sign variation in real projective space},
  author = {John Machacek},
  journal= {arXiv preprint arXiv:1909.04640},
  year   = {2023}
}

Comments

v2 contains corrections of minor typos and is the accepted version to appear in Ann. Inst. Henri Poincar\'e D