Matches in SemOpenAlex for { <https://semopenalex.org/work/W2055847176> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W2055847176 endingPage "343" @default.
- W2055847176 startingPage "319" @default.
- W2055847176 abstract "Let A be a central arrangement of hyperplanes in Cn , let M(A) be the complement of A , and let L(A) be the intersection lattice of A . For X in L(A) we set AX={H∈A:H⫆X} , and A/X={H/X:H∈AX} , and AX={H∩X:H∈AAX} . We exhibit natural embeddings of M(AX) in M(A) that give rise to monomorphisms from π1(M(AX)) to π1(M(A)) . We call the images of these monomorphisms intersection subgroups of type X and prove that they form a conjugacy class of subgroups of π1(M(A)) . Recall that X in L(A) is modular if X+Y is an element of L(A) for all Y in L(A) . We call X in L(A) supersolvable if there exists a chain 0⫅X1⫅⋯⫅Xd=X in L(A) such that Xμ is modular and dimXμ=μ for all μ=1,…,d . Assume that X is supersolvable and view π1(M(AX)) as an intersection subgroup of type X of π1(M(A)) . Recall that the commensurator of a subgroup S in a group G is the set of a in G such that S∩aSa−1 has finite index in both S and aSa−1 . The main result of this paper is the characterization of the centralizer, the normalizer, and the commensurator of π1(M(AX)) in π1(M(A)) . More precisely, we exhibit an embedding of π1(M(AX)) in π1(M(A)) and prove: (1) π1(M(AX))∩π1(M(AX))={1} and π1(M(AX)) is included in the centralizer of π1(M(AX)) in π1(M(A)) ; (2) the normalizer is equal to the commensurator and is equal to the direct product of π1(M(AX)) and π1(M(AX)) ; (3) the centralizer is equal to the direct product of π1(M(AX)) and the center of π1(M(AX)) . Our study starts with an investigation of the projection p:M(A)→M(A/X) induced by the projection Cn→Cn/X . We prove in particular that this projection is a locally trivial C∞ fibration if X is modular, and deduce some exact sequences involving the fundamental groups of the complements of A , of A/X , and of some (affine) arrangement Az0X ." @default.
- W2055847176 created "2016-06-24" @default.
- W2055847176 creator A5054400690 @default.
- W2055847176 date "2000-08-01" @default.
- W2055847176 modified "2023-09-26" @default.
- W2055847176 title "Intersection subgroups of complex hyperplane arrangements" @default.
- W2055847176 doi "https://doi.org/10.1016/s0166-8641(99)00068-1" @default.
- W2055847176 hasPublicationYear "2000" @default.
- W2055847176 type Work @default.
- W2055847176 sameAs 2055847176 @default.
- W2055847176 citedByCount "9" @default.
- W2055847176 countsByYear W20558471762014 @default.
- W2055847176 countsByYear W20558471762019 @default.
- W2055847176 countsByYear W20558471762020 @default.
- W2055847176 countsByYear W20558471762021 @default.
- W2055847176 crossrefType "journal-article" @default.
- W2055847176 hasAuthorship W2055847176A5054400690 @default.
- W2055847176 hasConcept C104317684 @default.
- W2055847176 hasConcept C112313634 @default.
- W2055847176 hasConcept C114614502 @default.
- W2055847176 hasConcept C127413603 @default.
- W2055847176 hasConcept C127716648 @default.
- W2055847176 hasConcept C146978453 @default.
- W2055847176 hasConcept C185592680 @default.
- W2055847176 hasConcept C188082640 @default.
- W2055847176 hasConcept C18903297 @default.
- W2055847176 hasConcept C2777299769 @default.
- W2055847176 hasConcept C33923547 @default.
- W2055847176 hasConcept C55493867 @default.
- W2055847176 hasConcept C64543145 @default.
- W2055847176 hasConcept C68693459 @default.
- W2055847176 hasConcept C75174853 @default.
- W2055847176 hasConcept C86803240 @default.
- W2055847176 hasConcept C87945829 @default.
- W2055847176 hasConceptScore W2055847176C104317684 @default.
- W2055847176 hasConceptScore W2055847176C112313634 @default.
- W2055847176 hasConceptScore W2055847176C114614502 @default.
- W2055847176 hasConceptScore W2055847176C127413603 @default.
- W2055847176 hasConceptScore W2055847176C127716648 @default.
- W2055847176 hasConceptScore W2055847176C146978453 @default.
- W2055847176 hasConceptScore W2055847176C185592680 @default.
- W2055847176 hasConceptScore W2055847176C188082640 @default.
- W2055847176 hasConceptScore W2055847176C18903297 @default.
- W2055847176 hasConceptScore W2055847176C2777299769 @default.
- W2055847176 hasConceptScore W2055847176C33923547 @default.
- W2055847176 hasConceptScore W2055847176C55493867 @default.
- W2055847176 hasConceptScore W2055847176C64543145 @default.
- W2055847176 hasConceptScore W2055847176C68693459 @default.
- W2055847176 hasConceptScore W2055847176C75174853 @default.
- W2055847176 hasConceptScore W2055847176C86803240 @default.
- W2055847176 hasConceptScore W2055847176C87945829 @default.
- W2055847176 hasIssue "3" @default.
- W2055847176 hasLocation W20558471761 @default.
- W2055847176 hasOpenAccess W2055847176 @default.
- W2055847176 hasPrimaryLocation W20558471761 @default.
- W2055847176 hasRelatedWork W1586644482 @default.
- W2055847176 hasRelatedWork W1646312071 @default.
- W2055847176 hasRelatedWork W1964873491 @default.
- W2055847176 hasRelatedWork W1978401076 @default.
- W2055847176 hasRelatedWork W2060489837 @default.
- W2055847176 hasRelatedWork W2091262374 @default.
- W2055847176 hasRelatedWork W2091529844 @default.
- W2055847176 hasRelatedWork W2128030693 @default.
- W2055847176 hasRelatedWork W2969081390 @default.
- W2055847176 hasRelatedWork W3015837531 @default.
- W2055847176 hasVolume "105" @default.
- W2055847176 isParatext "false" @default.
- W2055847176 isRetracted "false" @default.
- W2055847176 magId "2055847176" @default.
- W2055847176 workType "article" @default.