Cobordisms of fold maps of 4-manifolds into the space

TL;DR

This paper computes the cobordism group of fold maps from 4-manifolds into a space, providing a complete classification using geometric invariants, with various restrictions on singular fibers.

Contribution

It introduces a comprehensive calculation of the cobordism group for fold maps of 4-manifolds, including all restrictions on singular fibers, and identifies geometric invariants for classification.

Findings

Computed the oriented cobordism group of fold maps of 4-manifolds.

Established geometric invariants that classify the cobordism group.

Analyzed fold maps with all possible restrictions on singular fibers.

Abstract

We compute the oriented cobordism group of fold maps of 4-manifolds into the space with all the possible restrictions (and also with no restriction) to the singular fibers. We also give geometric invariants which describe completely the cobordism group of fold maps.