4 papers
A categorification for the characteristic polynomial of matroids
Takuya Saito, So Yamagata
In the present paper, we provide cohomology groups for matroids, as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-represe…
Non-vanishing of homotopy groups of Manin--Schechtman arrangements
Takuya Saito, So Yamagata
One of the central problems in the topology of hyperplane arrangements is determining whether the complement is a -space. In this paper, we study Manin--Schechtman arrange…
A lexicographic section of the braid arrangement and the modified Artin presentation
So Yamagata
We study a specific line arrangement obtained from a generic -section of the braid arrangement, and compute the fundamental group of its complement via braid monodromy. We show…
Mapping fiber, loop and suspension graphs in naive discrete homotopy theory
So Yamagata
Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their conn…