Todd polynomials and Hirzebruch numbers

TL;DR

This paper introduces a new formula for Todd polynomials using forgotten symmetric functions, simplifying the proof of Hirzebruch's original formula and offering new insights into Hirzebruch numbers.

Contribution

It presents a novel expression for Todd polynomials based on forgotten symmetric functions, connecting complex cobordisms to classical Hirzebruch formulas.

Findings

Simplified proof of Hirzebruch's formula for Todd polynomial denominators

New interpretations for Hirzebruch numbers

Connection between complex cobordisms and symmetric functions

Abstract

In 1956 Hirzebruch found an explicit formula for the denominators of the Todd polynomials, which was proved later in his joint work with Atiyah. We present a new formula for the Todd polynomials in terms of the ``forgotten symmetric functions", which follows from our previous work on complex cobordisms. In particular, this leads to a simpler proof of the Hirzebruch formula and provides new interpretations for the Hirzebruch numbers.