Coincidence theory in arbitrary codimensions: the minimizing problem

TL;DR

This paper explores the geometric theory of coincidences between smooth maps of arbitrary codimensions using normal bordism theory and pathspaces, providing new insights into the minimizing problem.

Contribution

It introduces a novel geometric approach to coincidence theory in arbitrary codimensions employing nonstabilized normal bordism and pathspace techniques.

Findings

Develops a framework for analyzing coincidences via normal bordism.

Provides methods to address the minimizing problem in coincidence theory.

Extends classical coincidence results to higher codimensions.

Abstract

Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.