Betti number bounds for fewnomial hypersurfaces via stratified Morse theory

TL;DR

This paper introduces a novel bound on the sum of Betti numbers for certain hypersurfaces defined by fewnomials, utilizing stratified Morse theory to improve understanding of their topological complexity.

Contribution

The authors develop a new bound for Betti numbers of fewnomial hypersurfaces using stratified Morse theory, advancing topological analysis of polynomial-defined manifolds.

Findings

New bound for Betti numbers of fewnomial hypersurfaces

Application of stratified Morse theory to manifolds with corners

Enhanced understanding of topological complexity in polynomial hypersurfaces

Abstract

We use stratified Morse theory for a manifold with corners to give a new bound for the sum of the Betti numbers of a hypersurface in R^n_> defined by a polynomial with n+l+1 terms.