---
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 f from K to R^n on a compact space
K that are invariant with respect to perturbations of f. The perturbations are
arbitrary continuous maps within L_infty distance r from f for a given r >
0. The main drawback of the approach is that the computability of well groups
was shown only when dim K = n or n = 1. 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 R^n by
f. In other words, well groups can be algorithmically approximated from below.
When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well
group is exact. For the second part, we find examples of maps f, f'' from K to
R^n 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: 10.4230/LIPIcs.SOCG.2015.842
bibo_volume: 34
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
dct_title: On computability and triviality of well groups@
...