Matches in SemOpenAlex for { <https://semopenalex.org/work/W4380993708> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W4380993708 abstract "Let $G$ be a group and $N$ a normal subgroup of $G$. We study the large scale behavior, not the exact values themselves, of the stable mixed commutator length $scl_{G,N}$ on the mixed commutator subgroup $[G,N]$; when $N=G$, $scl_{G,N}$ equals the stable commutator length $scl_G$ on the commutator subgroup $[G,G]$. For this purpose, we regard $scl_{G,N}$ not only as a function from $[G,N]$ to $mathbb{R}_{geq 0}$, but as a bi-invariant metric function $d^+_{scl_{G,N}}$ from $[G,N]times [G,N]$ to $mathbb{R}_{geq 0}$. Our main focus is coarse group theoretic structures of $([G,N],d^+_{scl_{G,N}})$. Our preliminary result (the absolute version) connects, via the Bavard duality, $([G,N],d^+_{scl_{G,N}})$ and the quotient vector space of the space of $G$-invariant quasimorphisms on $N$ over one of such homomorphisms. In particular, we prove that the dimension of this vector space equals the asymptotic dimension of $([G,N],d^+_{scl_{G,N}})$. Our main result is the comparative version: we connect the coarse kernel, formulated by Leitner and Vigolo, of the coarse homomorphism $iota_{G,N}colon ([G,N],d^+_{scl_{G,N}})to ([G,N],d^+_{scl_{G}})$; $ymapsto y$, and a certain quotient vector space $W(G,N)$ of the space of invariant quasimorphisms. Assume that $N=[G,G]$ and that $W(G,N)$ is finite dimensional with dimension $ell$. Then we prove that the coarse kernel of $iota_{G,N}$ is isomorphic to $mathbb{Z}^{ell}$ as a coarse group. In contrast to the absolute version, the space $W(G,N)$ is finite dimensional in many cases, including all $(G,N)$ with finitely generated $G$ and nilpotent $G/N$. As an application of our result, given a group homomorphism $varphicolon Gto H$ between finitely generated groups, we define an $mathbb{R}$-linear map `inside' the groups, which is dual to the naturally defined $mathbb{R}$-linear map from $W(H,[H,H])$ to $W(G,[G,G])$ induced by $varphi$." @default.
- W4380993708 created "2023-06-17" @default.
- W4380993708 creator A5023036020 @default.
- W4380993708 creator A5023133164 @default.
- W4380993708 creator A5054862921 @default.
- W4380993708 creator A5058458566 @default.
- W4380993708 creator A5017310297 @default.
- W4380993708 date "2023-06-14" @default.
- W4380993708 modified "2023-09-23" @default.
- W4380993708 title "Coarse group theoretic study on stable mixed commutator length" @default.
- W4380993708 doi "https://doi.org/10.48550/arxiv.2306.08618" @default.
- W4380993708 hasPublicationYear "2023" @default.
- W4380993708 type Work @default.
- W4380993708 citedByCount "0" @default.
- W4380993708 crossrefType "posted-content" @default.
- W4380993708 hasAuthorship W4380993708A5017310297 @default.
- W4380993708 hasAuthorship W4380993708A5023036020 @default.
- W4380993708 hasAuthorship W4380993708A5023133164 @default.
- W4380993708 hasAuthorship W4380993708A5054862921 @default.
- W4380993708 hasAuthorship W4380993708A5058458566 @default.
- W4380993708 hasBestOaLocation W43809937081 @default.
- W4380993708 hasConcept C105515060 @default.
- W4380993708 hasConcept C114614502 @default.
- W4380993708 hasConcept C121332964 @default.
- W4380993708 hasConcept C136119220 @default.
- W4380993708 hasConcept C140865510 @default.
- W4380993708 hasConcept C145620117 @default.
- W4380993708 hasConcept C190470478 @default.
- W4380993708 hasConcept C199422724 @default.
- W4380993708 hasConcept C202444582 @default.
- W4380993708 hasConcept C2781311116 @default.
- W4380993708 hasConcept C33676613 @default.
- W4380993708 hasConcept C33923547 @default.
- W4380993708 hasConcept C37914503 @default.
- W4380993708 hasConcept C4042151 @default.
- W4380993708 hasConcept C62520636 @default.
- W4380993708 hasConcept C73648015 @default.
- W4380993708 hasConcept C74193536 @default.
- W4380993708 hasConceptScore W4380993708C105515060 @default.
- W4380993708 hasConceptScore W4380993708C114614502 @default.
- W4380993708 hasConceptScore W4380993708C121332964 @default.
- W4380993708 hasConceptScore W4380993708C136119220 @default.
- W4380993708 hasConceptScore W4380993708C140865510 @default.
- W4380993708 hasConceptScore W4380993708C145620117 @default.
- W4380993708 hasConceptScore W4380993708C190470478 @default.
- W4380993708 hasConceptScore W4380993708C199422724 @default.
- W4380993708 hasConceptScore W4380993708C202444582 @default.
- W4380993708 hasConceptScore W4380993708C2781311116 @default.
- W4380993708 hasConceptScore W4380993708C33676613 @default.
- W4380993708 hasConceptScore W4380993708C33923547 @default.
- W4380993708 hasConceptScore W4380993708C37914503 @default.
- W4380993708 hasConceptScore W4380993708C4042151 @default.
- W4380993708 hasConceptScore W4380993708C62520636 @default.
- W4380993708 hasConceptScore W4380993708C73648015 @default.
- W4380993708 hasConceptScore W4380993708C74193536 @default.
- W4380993708 hasLocation W43809937081 @default.
- W4380993708 hasLocation W43809937082 @default.
- W4380993708 hasOpenAccess W4380993708 @default.
- W4380993708 hasPrimaryLocation W43809937081 @default.
- W4380993708 hasRelatedWork W1598346960 @default.
- W4380993708 hasRelatedWork W1995069357 @default.
- W4380993708 hasRelatedWork W2035733633 @default.
- W4380993708 hasRelatedWork W2048963143 @default.
- W4380993708 hasRelatedWork W2062886510 @default.
- W4380993708 hasRelatedWork W2095145437 @default.
- W4380993708 hasRelatedWork W2131685986 @default.
- W4380993708 hasRelatedWork W2293882952 @default.
- W4380993708 hasRelatedWork W3186026004 @default.
- W4380993708 hasRelatedWork W4298361533 @default.
- W4380993708 isParatext "false" @default.
- W4380993708 isRetracted "false" @default.
- W4380993708 workType "article" @default.