---
_id: '1252'
abstract:
- lang: eng
text: We study the homomorphism induced in homology by a closed correspondence between
topological spaces, using projections from the graph of the correspondence to
its domain and codomain. We provide assumptions under which the homomorphism induced
by an outer approximation of a continuous map coincides with the homomorphism
induced in homology by the map. In contrast to more classical results we do not
require that the projection to the domain have acyclic preimages. Moreover, we
show that it is possible to retrieve correct homological information from a correspondence
even if some data is missing or perturbed. Finally, we describe an application
to combinatorial maps that are either outer approximations of continuous maps
or reconstructions of such maps from a finite set of data points.
author:
- first_name: Shaun
full_name: Harker, Shaun
last_name: Harker
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from
a correspondence. *Proceedings of the American Mathematical Society*. 2016;144(4):1787-1801.
doi:10.1090/proc/12812
apa: Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing
a map on homology from a correspondence. *Proceedings of the American Mathematical
Society*, *144*(4), 1787–1801. https://doi.org/10.1090/proc/12812
chicago: 'Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk.
“Inducing a Map on Homology from a Correspondence.” *Proceedings of the American
Mathematical Society* 144, no. 4 (2016): 1787–1801. https://doi.org/10.1090/proc/12812.'
ieee: S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on
homology from a correspondence,” *Proceedings of the American Mathematical Society*,
vol. 144, no. 4, pp. 1787–1801, 2016.
ista: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology
from a correspondence. Proceedings of the American Mathematical Society. 144(4),
1787–1801.
mla: Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” *Proceedings
of the American Mathematical Society*, vol. 144, no. 4, American Mathematical
Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.
short: S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American
Mathematical Society 144 (2016) 1787–1801.
date_created: 2018-12-11T11:50:57Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2019-08-02T12:36:58Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/12812
intvolume: ' 144'
issue: '4'
language:
- iso: eng
month: '04'
oa_version: None
page: 1787 - 1801
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6075'
quality_controlled: '1'
status: public
title: Inducing a map on homology from a correspondence
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...