Matches in SemOpenAlex for { <https://semopenalex.org/work/W1895954743> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W1895954743 endingPage "164" @default.
- W1895954743 startingPage "126" @default.
- W1895954743 abstract "The concept of well group in a special but important case captures homological properties of the zero set of a continuous map $$f:Krightarrow {mathbb {R}}^n$$ 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 $${mathbb {R}}^n$$ 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 $$f,f':Krightarrow {mathbb {R}}^n$$ 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." @default.
- W1895954743 created "2016-06-24" @default.
- W1895954743 creator A5014115669 @default.
- W1895954743 creator A5075791550 @default.
- W1895954743 date "2016-05-31" @default.
- W1895954743 modified "2023-09-27" @default.
- W1895954743 title "On Computability and Triviality of Well Groups" @default.
- W1895954743 cites W130934891 @default.
- W1895954743 cites W154568157 @default.
- W1895954743 cites W1991566301 @default.
- W1895954743 cites W1993027581 @default.
- W1895954743 cites W1995509853 @default.
- W1895954743 cites W2020804487 @default.
- W1895954743 cites W2040211787 @default.
- W1895954743 cites W2041977310 @default.
- W1895954743 cites W2078634134 @default.
- W1895954743 cites W2143247392 @default.
- W1895954743 cites W2156468317 @default.
- W1895954743 cites W2321407057 @default.
- W1895954743 cites W2499046917 @default.
- W1895954743 cites W2963462120 @default.
- W1895954743 cites W4251616545 @default.
- W1895954743 doi "https://doi.org/10.1007/s00454-016-9794-2" @default.
- W1895954743 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/7175722" @default.
- W1895954743 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/32355388" @default.
- W1895954743 hasPublicationYear "2016" @default.
- W1895954743 type Work @default.
- W1895954743 sameAs 1895954743 @default.
- W1895954743 citedByCount "1" @default.
- W1895954743 countsByYear W18959547432023 @default.
- W1895954743 crossrefType "journal-article" @default.
- W1895954743 hasAuthorship W1895954743A5014115669 @default.
- W1895954743 hasAuthorship W1895954743A5075791550 @default.
- W1895954743 hasBestOaLocation W18959547431 @default.
- W1895954743 hasConcept C114614502 @default.
- W1895954743 hasConcept C118615104 @default.
- W1895954743 hasConcept C121332964 @default.
- W1895954743 hasConcept C138885662 @default.
- W1895954743 hasConcept C152062344 @default.
- W1895954743 hasConcept C17183583 @default.
- W1895954743 hasConcept C190470478 @default.
- W1895954743 hasConcept C202444582 @default.
- W1895954743 hasConcept C2778795013 @default.
- W1895954743 hasConcept C2780813799 @default.
- W1895954743 hasConcept C2781311116 @default.
- W1895954743 hasConcept C2991919592 @default.
- W1895954743 hasConcept C33923547 @default.
- W1895954743 hasConcept C37914503 @default.
- W1895954743 hasConcept C41895202 @default.
- W1895954743 hasConcept C62520636 @default.
- W1895954743 hasConceptScore W1895954743C114614502 @default.
- W1895954743 hasConceptScore W1895954743C118615104 @default.
- W1895954743 hasConceptScore W1895954743C121332964 @default.
- W1895954743 hasConceptScore W1895954743C138885662 @default.
- W1895954743 hasConceptScore W1895954743C152062344 @default.
- W1895954743 hasConceptScore W1895954743C17183583 @default.
- W1895954743 hasConceptScore W1895954743C190470478 @default.
- W1895954743 hasConceptScore W1895954743C202444582 @default.
- W1895954743 hasConceptScore W1895954743C2778795013 @default.
- W1895954743 hasConceptScore W1895954743C2780813799 @default.
- W1895954743 hasConceptScore W1895954743C2781311116 @default.
- W1895954743 hasConceptScore W1895954743C2991919592 @default.
- W1895954743 hasConceptScore W1895954743C33923547 @default.
- W1895954743 hasConceptScore W1895954743C37914503 @default.
- W1895954743 hasConceptScore W1895954743C41895202 @default.
- W1895954743 hasConceptScore W1895954743C62520636 @default.
- W1895954743 hasIssue "1" @default.
- W1895954743 hasLocation W18959547431 @default.
- W1895954743 hasLocation W18959547432 @default.
- W1895954743 hasLocation W18959547433 @default.
- W1895954743 hasLocation W18959547434 @default.
- W1895954743 hasLocation W18959547435 @default.
- W1895954743 hasLocation W18959547436 @default.
- W1895954743 hasOpenAccess W1895954743 @default.
- W1895954743 hasPrimaryLocation W18959547431 @default.
- W1895954743 hasRelatedWork W1516195074 @default.
- W1895954743 hasRelatedWork W1534977344 @default.
- W1895954743 hasRelatedWork W1895954743 @default.
- W1895954743 hasRelatedWork W1974849843 @default.
- W1895954743 hasRelatedWork W2084461749 @default.
- W1895954743 hasRelatedWork W2171176947 @default.
- W1895954743 hasRelatedWork W2326947865 @default.
- W1895954743 hasRelatedWork W2478145507 @default.
- W1895954743 hasRelatedWork W2949699615 @default.
- W1895954743 hasRelatedWork W4299811057 @default.
- W1895954743 hasVolume "56" @default.
- W1895954743 isParatext "false" @default.
- W1895954743 isRetracted "false" @default.
- W1895954743 magId "1895954743" @default.
- W1895954743 workType "article" @default.