Complex cobordism MU$^*[1/2]$ modulo MSU$^*[1/2]$ and related genera

TL;DR

This paper develops a new complex oriented cohomology theory based on the quotient of complex cobordism MU$^*[1/2]$ by ideals generated from special unitary cobordism MSU$^*[1/2]$, exploring their algebraic relations.

Contribution

It introduces a novel cohomology theory constructed as a quotient of MU$^*[1/2]$ by ideals related to MSU$^*[1/2]$, expanding the understanding of cobordism relations.

Findings

Defines a new commutative complex oriented cohomology theory.

Establishes algebraic relations between MU$^*[1/2]$ and MSU$^*[1/2]$.

Provides tools for computing related cobordism groups.

Abstract

This paper presents a commutative complex oriented cohomology theory with coefficients the quotient ring of complex cobordism MU$^*[1/2]$ modulo the ideal generated by any subsequence of any polynomial generators in special unitary cobordism MSU$^*[1/2]$ viewed as elements in MU$^*[1/2]$ by forgetful map.