LEADER 04430nam 22005893 450 001 9910957081003321 005 20231110220623.0 010 $a9781470471682$b(electronic bk.) 010 $z9781470453435 035 $a(MiAaPQ)EBC29378994 035 $a(Au-PeEL)EBL29378994 035 $a(CKB)24267881700041 035 $a(OCoLC)1336954268 035 $a(EXLCZ)9924267881700041 100 $a20220721d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSubset Currents on Surfaces 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$d©2022. 215 $a1 online resource (178 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.278 311 08$aPrint version: Sasaki, Dounnu Subset Currents on Surfaces Providence : American Mathematical Society,c2022 9781470453435 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. Background -- 1.2. Main results -- 1.3. Future study -- 1.4. Organization of article -- 1.5. Acknowledgements -- Chapter 2. Subset Currents on Hyperbolic Groups -- 2.1. Space of subset currents on hyperbolic group -- 2.2. Measure theory background -- Chapter 3. Volume Functionals on Kleinian Groups -- Chapter 4. Subgroups, Inclusion Maps and Finite Index Extension -- 4.1. Natural continuous linear maps between subgroups -- 4.2. Finite index extension of functionals -- Chapter 5. Intersection Number -- 5.1. Intersection number of closed curves -- 5.2. Intersection number of surfaces -- 5.3. Continuous extension of intersection number -- Chapter 6. Intersection Functional on Subset Currents -- Chapter 7. Projection from Subset Currents onto Geodesic Currents -- 7.1. Construction of projection -- 7.2. Application of projection -- Chapter 8. Denseness Property of Rational Subset Currents -- 8.1. Denseness property of free groups -- 8.2. Approximation by a sequence of subgroups -- 8.3. Denseness property of surface groups -- Bibliography -- Index -- Back Cover. 330 $a"Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic groups, which were introduced by Bonahon and have been successfully studied in the case of the fundamental group 1() of a compact hyperbolic surface . Kapovich and Nagnibeda particularly studied subset currents on free groups. In this article, we develop the theory of subset currents on 1(), which we call subset currents on . We prove that the space SC() of subset currents on is a measure-theoretic completion of the set of conjugacy classes of non-trivial finitely generated subgroups of 1(), each of which geometrically corresponds to a convex core of a covering space of . This result was proved by Kapovich-Nagnibeda in the case of free groups, and is also a generalization of Bonahon's result on geodesic currents on hyperbolic groups. We will also generalize several other results of them. Especially, we extend the (geometric) intersection number of two closed geodesics on to the intersection number of two convex cores on and, in addition, to a continuous R0-bilinear functional on SC()"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aFuchsian groups 606 $aRiemann surfaces 606 $aHyperbolic groups 606 $aErgodic theory 606 $aGroup theory and generalizations -- Special aspects of infinite or finite groups -- Hyperbolic groups and nonpositively curved groups$2msc 606 $aFunctions of a complex variable -- Riemann surfaces -- Fuchsian groups and automorphic functions$2msc 615 0$aFuchsian groups. 615 0$aRiemann surfaces. 615 0$aHyperbolic groups. 615 0$aErgodic theory. 615 7$aGroup theory and generalizations -- Special aspects of infinite or finite groups -- Hyperbolic groups and nonpositively curved groups. 615 7$aFunctions of a complex variable -- Riemann surfaces -- Fuchsian groups and automorphic functions. 676 $a515/.9 676 $a515.9 686 $a20F67$a30F35$2msc 700 $aSasaki$b Dounnu$01802279 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910957081003321 996 $aSubset Currents on Surfaces$94347857 997 $aUNINA LEADER 01304nam0 22002771i 450 001 UON00226788 005 20231205103440.554 100 $a20030730g19541959 |0itac50 ba 101 $aspa 102 $aMX 105 $a|||| ||||| 200 1 $aIndice critico de la literatura hispanoamericana$fAlberto Zum Felde 210 $aMexico$cGuarania$d1954-1959. 2 v. ; 24 cm Vol. 1: Los ensayistas 215 $aVol. 2: La narrativa. 410 1$1001UON00176386$12001 $aBiblioteca de pensadores y ensayistas americanos$1210 $aMexico$cGuarania 606 $aLetteratura ispano-americana$xCritica$3UONC041796$2FI 620 $aMX$dCiudad de México$3UONL003354 676 $a868.993$cLetteratura sudamericana in spagnolo$v21 700 1$aZUM FELDE$bAlberto$3UONV135773$0195083 712 $aGuarania$3UONV269014$4650 801 $aIT$bSOL$c20251121$gRICA 912 $aUON00226788 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI C 0230 $eSI MR 68285/1 7 0230 $sBuono 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI C 0210 $eSI MR 68285 7 0210 $sBuono 996 $aIndice critico de la literatura hispanoamericana$91271046 997 $aUNIOR