# Quasitoric totally normally split representatives in unitary cobordism ring

## TL;DR

This paper extends previous results in unitary cobordism theory by proving that every class in the unitary cobordism ring has a representative quasitoric manifold with specific splitting properties.

## Contribution

It generalizes earlier work by Ray and Buchstaber-Ray, Buchstaber-Panov-Ray, showing the existence of special representatives in the cobordism ring.

## Key findings

- Every class in the unitary cobordism ring has a quasitoric totally normally and tangentially split manifold representative.
- The results unify and extend prior theorems in the field.
- Provides new tools for studying the structure of the unitary cobordism ring.

## Abstract

The present paper generalises the results of Ray and Buchstaber-Ray, Buchstaber-Panov-Ray in unitary cobordism theory. I prove that any class $x\in \Omega^{*}_{U}$ of the unitary cobordism ring contains a quasitoric totally normally and tangentially split manifold.