Filtrations of tope spaces of oriented matroids

Algebra Seminar
Monday, September 25, 2023 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 006
Chi Ho Yuen – Oslo University –
Changxin Ding

Please Note: There will be a pre-seminar (aimed toward grad students and postdocs) from 11:00 am-11:30 am in Skiles 006.

Oriented matroids are matroids with extra sign data, and they are useful in the tropical study of real algebraic geometry. In order to study the topology of real algebraic hypersurfaces constructed from patchworking, Renaudineau and Shaw introduced an algebraically defined filtration of the tope space of an oriented matroid based on Quillen filtration. We will prove the equality between their filtration (together with the induced maps), the topologically defined Kalinin filtration, and the combinatorially defined Varchenko-Gelfand dual degree filtration over Z/2Z. We will also explain how the dual degree filtration can serve as a Z-coefficient version of the other two in this setting. This is joint work with Kris Shaw.