#### Document Type

Article

#### Article Version

Post-print

#### Publication Date

2012

#### Abstract

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in $\Z\oplus \Z_2$. We also show in each setting that the group of values for the index (either $\Z$ or $\Z\oplus \Z_2$) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which charaterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds.

#### Publication Title

Topology and its Applications

#### Repository Citation

Goncalves, Daciberg L. and Staecker, Christopher P., "Axioms for the coincidence index of maps between manifolds of the same dimension" (2012). *Math & Computer Science Faculty Publications*. 28.

http://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/28

#### Published Citation

Gonçalves, Daciberg L. and Staecker, P. Christopher, Axioms for the coincidence index of maps between manifolds of the same dimension. Topology and its Applications. Accepted for publication 2012.

Peer Reviewed

## Comments

Copyright Elsevier, Topology and its Applications

This is the author’s version of a work that was accepted for publication in Topology and its Appllications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version has been accepted for publication in Topology and its Applications . http://www.journals.elsevier.com/topology-and-its-applications/