The Hirzebruch $\chi_y$-genus and Poincare polynomial revisited

TL;DR

This paper explores the relationship between the Hirzebruch $hi_y$-genus and Poincare9 polynomial, deriving new results and refining existing ones by analyzing their shared features.

Contribution

It provides a unified investigation of the Hirzebruch $hi_y$-genus and Poincare9 polynomial, offering new insights and improvements on known results.

Findings

Derived new relationships between the $hi_y$-genus and Poincare9 polynomial.

Reproved and improved existing results related to these invariants.

Identified shared features that lead to novel mathematical results.

Abstract

The Hirzebruch $\chi_y$-genus and Poincare polynomial share some similar features. In this article we investigate two of their similar features simultaneously. Through this process we shall derive several new results as well as reprove and improve some known results.