On Computability and Triviality of Well Groups
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00454132" target="_blank" >RIV/67985807:_____/15:00454132 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.842" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.842</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.842" target="_blank" >10.4230/LIPIcs.SOCG.2015.842</a>
Alternative languages
Result language
angličtina
Original language name
On Computability and Triviality of Well Groups
Original language description
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 appro
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
31st International Symposium on Computational Geometry
ISBN
978-3-939897-83-5
ISSN
1868-8969
e-ISSN
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Number of pages
15
Pages from-to
842-856
Publisher name
Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl
Event location
Eindhoven
Event date
Jun 22, 2015
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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