# SU-bordism: structure results and geometric representatives

## TL;DR

This paper surveys the structure of the special unitary bordism ring using modern algebraic topology techniques and describes geometric representatives in SU-bordism classes via toric topology.

## Contribution

It combines classical geometric methods with advanced spectral sequence and formal group law techniques, and introduces geometric representatives using toric topology.

## Key findings

- Detailed description of SU-bordism ring structure
- Construction of geometric representatives in SU-bordism classes
- Integration of classical and modern topological methods

## Abstract

In the first part of this survey we give a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner-Floyd, Wall and Stong with the Adams-Novikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 work of Novikov. In the second part we use toric topology to describe geometric representatives in SU-bordism classes, including toric, quasitoric and Calabi-Yau manifolds.