Overview

Original Research

ON THE GEOMETRY OF MATROIDS AND FLOWS ON THEM

T.VENKATESH 1, and SHRUTI KAMALAKAR. GOVEKAR 2.

Vol 19, No 03 ( 2024 )   |  DOI: 10.5281/zenodo.10848135   |   Author Affiliation: RTD. Professor, Department of Mathematics and Director, Mathematical Sciences Institute Belagavi, Karnataka, India 1; Research Scholar, Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, India 2.   |   Licensing: CC 4.0   |   Pg no: 386-389   |   Published on: 14-03-2024

Abstract

Discrete version of manifolds lead to some combinatorial structures of the manifold and it is this aspect of the problem that lead to rich investigations. Matroids came to fore purely as combinatorial theme with a firm geometry behind it. In our investigations we have considered discrete versions of low dimensional topological manifolds and developed few ideas relating to certain flows on them to locate invariant sets. Mainly the Anasov diffeomorphisms. It will be presented in two parts the first paper will be the description of matriods and their role in Linear algebraic setting and then graph theoretic setting. Not much is dealt when it comes to the geometry but we assume that the underlying manifold is smooth .We have specifically given one interesting case for the stability of the invariant sets. Also we have a family of algebraic varieties to this we want to attach a family of combinatorial objects and these are our convex polytopes

Keywords

Matroids, Topological Manifolds, Convex Polytopes