---
res:
bibo_abstract:
- 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map (Formula presented.) on a compact
space K that are invariant with respect to perturbations of f. The perturbations
are arbitrary continuous maps within (Formula presented.) distance r from f for
a given (Formula presented.). The main drawback of the approach is that the computability
of well groups was shown only when (Formula presented.) or (Formula presented.).
Our contribution to the theory of well groups is twofold: on the one hand we improve
on the computability issue, but on the other hand we present a range of examples
where the well groups are incomplete invariants, that is, fail to capture certain
important robust properties of the zero set. For the first part, we identify a
computable subgroup of the well group that is obtained by cap product with the
pullback of the orientation of (Formula presented.) by f. In other words, well
groups can be algorithmically approximated from below. When f is smooth and (Formula
presented.), our approximation of the (Formula presented.)th well group is exact.
For the second part, we find examples of maps (Formula presented.) with all well
groups isomorphic but whose perturbations have different zero sets. We discuss
on a possible replacement of the well groups of vector valued maps by an invariant
of a better descriptive power and computability status.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Peter
foaf_name: Franek, Peter
foaf_surname: Franek
foaf_workInfoHomepage: http://www.librecat.org/personId=473294AE-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Marek
foaf_name: Krcál, Marek
foaf_surname: Krcál
foaf_workInfoHomepage: http://www.librecat.org/personId=33E21118-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1007/s00454-016-9794-2
bibo_issue: '1'
bibo_volume: 56
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: On computability and triviality of well groups@
...