Algebraic Shifting and f-Vector Theory

TL;DR

This thesis explores algebraic shifting techniques and their applications to the f-vector theory of simplicial complexes and graded posets, providing partial results related to the g-conjecture for simplicial spheres.

Contribution

It introduces new approaches and partial results in algebraic shifting and f-vector theory, advancing understanding of the g-conjecture for simplicial spheres.

Findings

Partial results towards the g-conjecture for simplicial spheres

Development of algebraic shifting methods for graded posets

Insights into the structure of f-vectors in simplicial complexes

Abstract

This thesis focuses on algebraic shifting and its applications to f-vector theory of simplicial complexes and more general graded posets. In particular, several approaches and partial results concerning the g-conjecture for simplicial spheres are presented here.