On Computability and Triviality of Well Groups

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Computability and Triviality of Well Groups

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

On Computability and Triviality of Well Groups

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

31st International Symposium on Computational Geometry

ISBN

978-3-939897-83-5

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

15

Strana od-do

842-856

Název nakladatele

Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Eindhoven

Datum konání akce

22. 6. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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