FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2205200405> ?p ?o ?g. }

• W2205200405 abstract "Scott proved that if $Sigma$ is a closed surface with a hyperbolic metric $rho$, then for every closed geodesic $gamma$ on $Sigma$ there exists a finite cover of $Sigma$ where $gamma$ lifts to a simple closed geodesic. Define $f_rho(L)ge 0$ to be the smallest monotone nondecreasing such that every closed geodesic of length $le L$ on $Sigma$ lifts to a simple closed geodesic in a cover of $Sigma$ of degree $le f_rho(L)$. A result of Patel implies that for every hyperbolic structure $rho$ on $Sigma$ there exists $K=K(rho)>0$ such that $f_rho(L)le KL$ for all $L>0$. We prove that there exist $c=c(rho)>0$ such that $f_rho(L)ge c log^{1/3} L$ for all large $L$. We obtain a similar lower bound for the $f_Sigma$ defined analogously to $f_rho$ but using the self-intersection number of closed curves on $Sigma$. These results are derived from several related results we establish for free groups. Thus we define, study and obtain lower bounds for the index function $f(n)$ and the simplicity index function $f_0(n)$ for the free group $F_N=F(a_1,dots, a_N)$ of finite rank $Nge 2$. The primitivity index $f(n)$ is the smallest monotone non-decreasing $f(n)ge 0$ such that for every nontrivial freely reduced word $win F_N$ of length $le n$ there is a subgroup $Hle F_N$ of index $le f(n)$ such that $win H$ and that $w$ is a primitive element (i.e. an element of a free basis) of $H$. The $f_0(n)$ is defined similarly except that instead of $w$ being primitive in $H$ we require that $w$ belongs to a proper free factor of $H$. The lower bounds for $f(n)$ and $f_0(n)$ are obtained via probabilistic methods, by estimating from below the emph{simplicity index} for a sufficiently element $w_nin F_N$ produced by a simple non-backtracking random walk of length $n$ on $F_N$." @default.
• W2205200405 created "2016-06-24" @default.
• W2205200405 creator A5000945965 @default.
• W2205200405 creator A5023281472 @default.
• W2205200405 date "2014-11-20" @default.
• W2205200405 modified "2023-09-27" @default.
• W2205200405 title "The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces" @default.
• W2205200405 cites W1974386361 @default.
• W2205200405 cites W1982041505 @default.
• W2205200405 cites W2039071938 @default.
• W2205200405 cites W2040037490 @default.
• W2205200405 cites W2050733003 @default.
• W2205200405 cites W2051115580 @default.
• W2205200405 cites W2054631814 @default.
• W2205200405 cites W2065954935 @default.
• W2205200405 cites W2070983130 @default.
• W2205200405 cites W2117159270 @default.
• W2205200405 cites W2165003413 @default.
• W2205200405 cites W2327432488 @default.
• W2205200405 cites W2409929839 @default.
• W2205200405 cites W2471750801 @default.
• W2205200405 cites W2593183794 @default.
• W2205200405 cites W2964293047 @default.
• W2205200405 cites W3101681265 @default.
• W2205200405 cites W3102790340 @default.
• W2205200405 cites W3105418068 @default.
• W2205200405 cites W3106216168 @default.
• W2205200405 cites W2951677361 @default.
• W2205200405 hasPublicationYear "2014" @default.
• W2205200405 type Work @default.
• W2205200405 sameAs 2205200405 @default.
• W2205200405 citedByCount "6" @default.
• W2205200405 countsByYear W22052004052015 @default.
• W2205200405 countsByYear W22052004052016 @default.
• W2205200405 countsByYear W22052004052017 @default.
• W2205200405 crossrefType "posted-content" @default.
• W2205200405 hasAuthorship W2205200405A5000945965 @default.
• W2205200405 hasAuthorship W2205200405A5023281472 @default.
• W2205200405 hasConcept C114614502 @default.
• W2205200405 hasConcept C121332964 @default.
• W2205200405 hasConcept C127413603 @default.
• W2205200405 hasConcept C134306372 @default.
• W2205200405 hasConcept C14036430 @default.
• W2205200405 hasConcept C164226766 @default.
• W2205200405 hasConcept C165818556 @default.
• W2205200405 hasConcept C24890656 @default.
• W2205200405 hasConcept C2524010 @default.
• W2205200405 hasConcept C2775997480 @default.
• W2205200405 hasConcept C2778049214 @default.
• W2205200405 hasConcept C2780428219 @default.
• W2205200405 hasConcept C2834757 @default.
• W2205200405 hasConcept C33923547 @default.
• W2205200405 hasConcept C62520636 @default.
• W2205200405 hasConcept C77553402 @default.
• W2205200405 hasConcept C78458016 @default.
• W2205200405 hasConcept C78519656 @default.
• W2205200405 hasConcept C86803240 @default.
• W2205200405 hasConceptScore W2205200405C114614502 @default.
• W2205200405 hasConceptScore W2205200405C121332964 @default.
• W2205200405 hasConceptScore W2205200405C127413603 @default.
• W2205200405 hasConceptScore W2205200405C134306372 @default.
• W2205200405 hasConceptScore W2205200405C14036430 @default.
• W2205200405 hasConceptScore W2205200405C164226766 @default.
• W2205200405 hasConceptScore W2205200405C165818556 @default.
• W2205200405 hasConceptScore W2205200405C24890656 @default.
• W2205200405 hasConceptScore W2205200405C2524010 @default.
• W2205200405 hasConceptScore W2205200405C2775997480 @default.
• W2205200405 hasConceptScore W2205200405C2778049214 @default.
• W2205200405 hasConceptScore W2205200405C2780428219 @default.
• W2205200405 hasConceptScore W2205200405C2834757 @default.
• W2205200405 hasConceptScore W2205200405C33923547 @default.
• W2205200405 hasConceptScore W2205200405C62520636 @default.
• W2205200405 hasConceptScore W2205200405C77553402 @default.
• W2205200405 hasConceptScore W2205200405C78458016 @default.
• W2205200405 hasConceptScore W2205200405C78519656 @default.
• W2205200405 hasConceptScore W2205200405C86803240 @default.
• W2205200405 hasLocation W22052004051 @default.
• W2205200405 hasOpenAccess W2205200405 @default.
• W2205200405 hasPrimaryLocation W22052004051 @default.
• W2205200405 hasRelatedWork W1921160739 @default.
• W2205200405 hasRelatedWork W1981199266 @default.
• W2205200405 hasRelatedWork W2051115580 @default.
• W2205200405 hasRelatedWork W2065954935 @default.
• W2205200405 hasRelatedWork W2081145785 @default.
• W2205200405 hasRelatedWork W2085708173 @default.
• W2205200405 hasRelatedWork W2373449067 @default.
• W2205200405 hasRelatedWork W2471933635 @default.
• W2205200405 hasRelatedWork W2550244391 @default.
• W2205200405 hasRelatedWork W2593183794 @default.
• W2205200405 hasRelatedWork W2739337143 @default.
• W2205200405 hasRelatedWork W2770574960 @default.
• W2205200405 hasRelatedWork W2900740800 @default.
• W2205200405 hasRelatedWork W2950767125 @default.
• W2205200405 hasRelatedWork W2963337410 @default.
• W2205200405 hasRelatedWork W3102345637 @default.
• W2205200405 hasRelatedWork W3103409668 @default.
• W2205200405 hasRelatedWork W3198419789 @default.
• W2205200405 hasRelatedWork W3207974594 @default.
• W2205200405 hasRelatedWork W88420397 @default.
• W2205200405 isParatext "false" @default.

• next