FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4214544959> ?p ?o ?g. }

• W4214544959 endingPage "626" @default.
• W4214544959 startingPage "605" @default.
• W4214544959 abstract "Abstract We study the Bieri–Neumann–Strebel–Renz invariants and we prove the following criterion: for groups H and K of type <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>F</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>P</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:math> {FP_{n}} such that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mo>⊆</m:mo> <m:mi>K</m:mi> <m:mo>⊆</m:mo> <m:mi>H</m:mi> </m:mrow> </m:math> {[H,H]subseteq Ksubseteq H} and a character <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>χ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>K</m:mi> <m:mo>→</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:mrow> </m:math> {chi:Ktomathbb{R}} with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>χ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {chi([H,H])=0} , we have <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mi>χ</m:mi> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mo>∈</m:mo> <m:mrow> <m:msup> <m:mi mathvariant=normal>Σ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo>,</m:mo> <m:mi>ℤ</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {[chi]inSigma^{n}(K,mathbb{Z})} if and only if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mi>μ</m:mi> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mo>∈</m:mo> <m:mrow> <m:msup> <m:mi mathvariant=normal>Σ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:mi>ℤ</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {[mu]inSigma^{n}(H,mathbb{Z})} for every character <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>μ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>H</m:mi> <m:mo>→</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:mrow> </m:math> {mu:Htomathbb{R}} that extends χ. The same holds for the homotopical invariants <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi mathvariant=normal>Σ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mo>-</m:mo> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {Sigma^{n}(-)} when K and H are groups of type <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>F</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> {F_{n}} . We use these criteria to complete the description of the Σ-invariants of the Bieri–Stallings groups <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>G</m:mi> <m:mi>m</m:mi> </m:msub> </m:math> {G_{m}} , and more generally to describe the Σ-invariants of the Bestvina–Brady groups. We also show that the “only if” direction of the above criterion holds if we assume only that K is a subnormal subgroup of H , where both groups are of type <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>F</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>P</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:math> {FP_{n}} . We apply this last result to wreath products." @default.
• W4214544959 created "2022-03-02" @default.
• W4214544959 creator A5000268378 @default.
• W4214544959 creator A5034188406 @default.
• W4214544959 date "2022-03-01" @default.
• W4214544959 modified "2023-10-17" @default.
• W4214544959 title "On the Bieri–Neumann–Strebel–Renz Σ-invariants of the Bestvina–Brady groups" @default.
• W4214544959 cites W164273335 @default.
• W4214544959 cites W1965055378 @default.
• W4214544959 cites W1988201431 @default.
• W4214544959 cites W1989276000 @default.
• W4214544959 cites W1998833490 @default.
• W4214544959 cites W2005047182 @default.
• W4214544959 cites W2007691791 @default.
• W4214544959 cites W2020077392 @default.
• W4214544959 cites W2023806008 @default.
• W4214544959 cites W2025687961 @default.
• W4214544959 cites W2047298806 @default.
• W4214544959 cites W2059683613 @default.
• W4214544959 cites W2061741468 @default.
• W4214544959 cites W2063331588 @default.
• W4214544959 cites W2067463721 @default.
• W4214544959 cites W2068115559 @default.
• W4214544959 cites W2078778823 @default.
• W4214544959 cites W2081925316 @default.
• W4214544959 cites W2103506608 @default.
• W4214544959 cites W2113091533 @default.
• W4214544959 cites W2145656857 @default.
• W4214544959 cites W2322845281 @default.
• W4214544959 cites W2328309467 @default.
• W4214544959 cites W2554135471 @default.
• W4214544959 cites W2572123340 @default.
• W4214544959 cites W2755633315 @default.
• W4214544959 cites W2759798053 @default.
• W4214544959 cites W2963207226 @default.
• W4214544959 cites W2963536573 @default.
• W4214544959 cites W2964089741 @default.
• W4214544959 cites W2964164469 @default.
• W4214544959 cites W2971973187 @default.
• W4214544959 cites W3045415672 @default.
• W4214544959 cites W3104644135 @default.
• W4214544959 cites W3193334815 @default.
• W4214544959 cites W4205718705 @default.
• W4214544959 doi "https://doi.org/10.1515/forum-2021-0059" @default.
• W4214544959 hasPublicationYear "2022" @default.
• W4214544959 type Work @default.
• W4214544959 citedByCount "0" @default.
• W4214544959 crossrefType "journal-article" @default.
• W4214544959 hasAuthorship W4214544959A5000268378 @default.
• W4214544959 hasAuthorship W4214544959A5034188406 @default.
• W4214544959 hasConcept C114614502 @default.
• W4214544959 hasConcept C121332964 @default.
• W4214544959 hasConcept C33923547 @default.
• W4214544959 hasConceptScore W4214544959C114614502 @default.
• W4214544959 hasConceptScore W4214544959C121332964 @default.
• W4214544959 hasConceptScore W4214544959C33923547 @default.
• W4214544959 hasFunder F4320320997 @default.
• W4214544959 hasFunder F4320322025 @default.
• W4214544959 hasIssue "3" @default.
• W4214544959 hasLocation W42145449591 @default.
• W4214544959 hasOpenAccess W4214544959 @default.
• W4214544959 hasPrimaryLocation W42145449591 @default.
• W4214544959 hasRelatedWork W1119550 @default.
• W4214544959 hasRelatedWork W11663883 @default.
• W4214544959 hasRelatedWork W12148668 @default.
• W4214544959 hasRelatedWork W13308840 @default.
• W4214544959 hasRelatedWork W13544095 @default.
• W4214544959 hasRelatedWork W20690647 @default.
• W4214544959 hasRelatedWork W22592713 @default.
• W4214544959 hasRelatedWork W24176775 @default.
• W4214544959 hasRelatedWork W4950985 @default.
• W4214544959 hasRelatedWork W7215141 @default.
• W4214544959 hasVolume "34" @default.
• W4214544959 isParatext "false" @default.
• W4214544959 isRetracted "false" @default.
• W4214544959 workType "article" @default.