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Volumn 6, Issue 4, 1997, Pages 313-326

Group Cohomology, Harmonic Functions and the First L2-Betti Number

Author keywords

Ends; Group cohomology; Harmonic functions; L2 cohomology

Indexed keywords


EID: 0031519820     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017974406074     Document Type: Article
Times cited : (65)

References (38)
  • 1
    • 84974002130 scopus 로고
    • On the fundamental group of a compact Kähler manifold
    • Arapura, D., Bressler, P. and Ramachandran, M.: On the fundamental group of a compact Kähler manifold, Duke Math. J. 68 (1992), 477-488.
    • (1992) Duke Math. J. , vol.68 , pp. 477-488
    • Arapura, D.1    Bressler, P.2    Ramachandran, M.3
  • 2
    • 0011566561 scopus 로고
    • Sur la cohomologie continue des groupes localement compacts
    • Blanc, P.: Sur la cohomologie continue des groupes localement compacts, Ann. Scient. Ec. Norm. Sup. (4ème série) 12 (1979), 137-168.
    • (1979) Ann. Scient. Ec. Norm. Sup. (4ème Série) , vol.12 , pp. 137-168
    • Blanc, P.1
  • 3
    • 0003365005 scopus 로고
    • Existence of discrete cocompact subgroups of reductive groups over local fieds
    • Borel, A. and Harder, G.: Existence of discrete cocompact subgroups of reductive groups over local fieds, J. reine angew. Math. 298 (1978), 53-64.
    • (1978) J. Reine Angew. Math. , vol.298 , pp. 53-64
    • Borel, A.1    Harder, G.2
  • 4
    • 0002872687 scopus 로고
    • Continuous cohomology, discrete subgroups and representations of reductive groups
    • Princeton Univ. Press
    • Borel, A. and Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. Math. Stud., Princeton Univ. Press, 1980.
    • (1980) Ann. Math. Stud.
    • Borel, A.1    Wallach, N.2
  • 6
    • 0039807224 scopus 로고
    • Infinite graphs with nonconstant Dirichlet finite harmonic functions
    • Cartwright, D. I. and Woess, W.: Infinite graphs with nonconstant Dirichlet finite harmonic functions, SIAM J. Disc. Math. 5 (1992), 380-385.
    • (1992) SIAM J. Disc. Math. , vol.5 , pp. 380-385
    • Cartwright, D.I.1    Woess, W.2
  • 7
    • 84972494180 scopus 로고
    • 2-cohomology and the Gauss-Bonnet theorem for open manifolds
    • 2-cohomology and the Gauss-Bonnet theorem for open manifolds, J. Differ. Geometry 21 (1985), 1-34.
    • (1985) J. Differ. Geometry , vol.21 , pp. 1-34
    • Cheeger, J.1    Gromov, M.2
  • 8
    • 0001757439 scopus 로고
    • 2-cohomology and group cohomology
    • 2-cohomology and group cohomology, Topology 25 (1986), 189-215.
    • (1986) Topology , vol.25 , pp. 189-215
    • Cheeger, J.1    Gromov, M.2
  • 10
    • 0000127272 scopus 로고
    • 2-index theorem for homogeneous spaces of Lie groups
    • 2-index theorem for homogeneous spaces of Lie groups, Ann. Math. 115 (1982), 291-330.
    • (1982) Ann. Math. , vol.115 , pp. 291-330
    • Connes, A.1    Moscovici, H.2
  • 11
    • 0000474439 scopus 로고
    • 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus et représentations
    • Delorme, P.: 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus et représentations, Bull. Soc. Math. France 105 (1977), 281-336.
    • (1977) Bull. Soc. Math. France , vol.105 , pp. 281-336
    • Delorme, P.1
  • 12
    • 0042952519 scopus 로고
    • Lois de Kirchhoff et fonctions discrètes harmoniques
    • Eckmann, B.: Lois de Kirchhoff et fonctions discrètes harmoniques, Bull. Soc. Vaud. Sc. Nat. 63 (1945), 67-78.
    • (1945) Bull. Soc. Vaud. Sc. Nat. , vol.63 , pp. 67-78
    • Eckmann, B.1
  • 14
    • 0003014190 scopus 로고
    • Sur le groupe fondamental d'une variété kählérienne
    • Sér. I
    • Gromov, M.: Sur le groupe fondamental d'une variété kählérienne, C. R. Acad. Sci. Paris 308 Sér. I (1989), 67-70.
    • (1989) C. R. Acad. Sci. Paris , vol.308 , pp. 67-70
    • Gromov, M.1
  • 15
    • 0002874575 scopus 로고
    • Asymptotic invariants of infinite groups
    • London Math. Soc.
    • Gromov, M.: Asymptotic invariants of infinite groups, Lect. Notes Ser. 182, London Math. Soc. 1993.
    • (1993) Lect. Notes Ser. , vol.182
    • Gromov, M.1
  • 16
    • 0010068634 scopus 로고
    • Sur la cohomologie des groupes topologiques II
    • Guichardet, A.: Sur la cohomologie des groupes topologiques II, Bull. Sc. Math. (2ème série) 96 (1972), 305-332.
    • (1972) Bull. Sc. Math. (2ème Série) , vol.96 , pp. 305-332
    • Guichardet, A.1
  • 17
    • 0009454347 scopus 로고
    • Etude de la 1-cohomologie et de la topologie du dual pour les groupes de Lie à radical abélien
    • Guichardet, A.: Etude de la 1-cohomologie et de la topologie du dual pour les groupes de Lie à radical abélien, Math. Ann. 228 (1977), 215-232.
    • (1977) Math. Ann. , vol.228 , pp. 215-232
    • Guichardet, A.1
  • 19
    • 0003229265 scopus 로고
    • La propriété (T) de Kazhdan pour les groupes localement compacts
    • Soc. Math. France
    • de la Harpe, P. and Valette, A.: La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France 1989.
    • (1989) Astérisque , vol.175
    • De La Harpe, P.1    Valette, A.2
  • 20
    • 51249166573 scopus 로고
    • On the spectrum of the sum of generators for a finitely generated group
    • de la Harpe, P., Robertson, A. G. and Valette, A.: On the spectrum of the sum of generators for a finitely generated group, Israel J. Math. 81 (1993), 65-96.
    • (1993) Israel J. Math. , vol.81 , pp. 65-96
    • De La Harpe, P.1    Robertson, A.G.2    Valette, A.3
  • 21
    • 51249193228 scopus 로고
    • Enden offener Räume und unendliche diskontinuierliche Gruppen
    • Hopf, H.: Enden offener Räume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv. 16 (1943), 81-100.
    • (1943) Comment. Math. Helv. , vol.16 , pp. 81-100
    • Hopf, H.1
  • 22
    • 0038454130 scopus 로고
    • Ends of groups and the associated first cohomology groups
    • Houghton, C. H.: Ends of groups and the associated first cohomology groups, J. London Math. Soc. 6 (1972), 81-92.
    • (1972) J. London Math. Soc. , vol.6 , pp. 81-92
    • Houghton, C.H.1
  • 23
    • 0042451531 scopus 로고
    • Property T for discrete groups in terms of their regular representation
    • Jolissaint, P.: Property T for discrete groups in terms of their regular representation, Math. Ann. 297 (1993), 539-551.
    • (1993) Math. Ann. , vol.297 , pp. 539-551
    • Jolissaint, P.1
  • 24
    • 38149146873 scopus 로고
    • 2-Betti numbers of mapping tori and groups
    • 2-Betti numbers of mapping tori and groups, Topology 33 (1994), 203-214.
    • (1994) Topology , vol.33 , pp. 203-214
    • Lück, W.1
  • 25
    • 0000445261 scopus 로고
    • 2-invariants by their finite-dimensional analogues
    • 2-invariants by their finite-dimensional analogues, GAFA 4 (1994), 455-481.
    • (1994) GAFA , vol.4 , pp. 455-481
    • Lück, W.1
  • 26
    • 84963048955 scopus 로고
    • Transient random walks on graphs and metric spaces with applications to hyperbolic surfaces
    • Markvorsen, S., McGuinness, S. and Thomassen, C.: Transient random walks on graphs and metric spaces with applications to hyperbolic surfaces, Proc. London Math. Soc. (3) 64 (1992), 1-20.
    • (1992) Proc. London Math. Soc. , vol.64 , Issue.3 , pp. 1-20
    • Markvorsen, S.1    McGuinness, S.2    Thomassen, C.3
  • 27
    • 0041449386 scopus 로고
    • A numerical invariant for finitely generated groups via actions on graphs
    • Paschke, W. L.: A numerical invariant for finitely generated groups via actions on graphs, Math. Scand. 72 (1993), 148-160.
    • (1993) Math. Scand. , vol.72 , pp. 148-160
    • Paschke, W.L.1
  • 28
    • 0001670235 scopus 로고
    • An invariant for finitely presented ℂG-modules
    • Paschke, W. L.: An invariant for finitely presented ℂG-modules, Math. Ann. 301 (1995), 325-337.
    • (1995) Math. Ann. , vol.301 , pp. 325-337
    • Paschke, W.L.1
  • 29
    • 0001544948 scopus 로고
    • 1-cohomologie de représentations induites
    • Pichaud, J.: 1-cohomologie de représentations induites, J. Maths. Pures et Appl. 56 (1977), 339-366.
    • (1977) J. Maths. Pures et Appl. , vol.56 , pp. 339-366
    • Pichaud, J.1
  • 30
    • 80053073516 scopus 로고
    • Groupes discrets
    • Springer-Verlag, Berlin
    • Poenaru, V.: Groupes discrets, Lect. Notes in Math. 421, Springer-Verlag, Berlin, 1974.
    • (1974) Lect. Notes in Math. , vol.421
    • Poenaru, V.1
  • 31
    • 0039453601 scopus 로고
    • 1-factors and unitary representations of Kazhdan groups
    • 1-factors and unitary representations of Kazhdan groups, Math. Ann. 296 (1993), 547-555.
    • (1993) Math. Ann. , vol.296 , pp. 547-555
    • Robertson, A.G.1
  • 32
    • 84968483712 scopus 로고
    • Rough isometries and Dirichlet finite harmonic functions on graphs
    • Soardi, P. M.: Rough isometries and Dirichlet finite harmonic functions on graphs, Proc. Amer Math. Soc. 119 (1993), 1239-1248.
    • (1993) Proc. Amer Math. Soc. , vol.119 , pp. 1239-1248
    • Soardi, P.M.1
  • 33
    • 0038454129 scopus 로고
    • Uniqueness of currents in infinite resistive networks
    • Soardi, P. M. and Woess, W.: Uniqueness of currents in infinite resistive networks, Discrete Applied Math. 31 (1991), 37-49.
    • (1991) Discrete Applied Math. , vol.31 , pp. 37-49
    • Soardi, P.M.1    Woess, W.2
  • 34
    • 0001480151 scopus 로고
    • Groups of cohomological dimension one
    • Swan, R. G.: Groups of cohomological dimension one, J. Algebra 12 (1969), 585-601.
    • (1969) J. Algebra , vol.12 , pp. 585-601
    • Swan, R.G.1
  • 36
    • 0011052127 scopus 로고
    • W*-algebras and nonabelian harmonic analysis
    • Walter, M. E.: W*-algebras and nonabelian harmonic analysis, J. Funct. Anal. 11 (1972), 17-38.
    • (1972) J. Funct. Anal. , vol.11 , pp. 17-38
    • Walter, M.E.1
  • 37
    • 0002768694 scopus 로고
    • Random walks on infinite graphs and groups - A survey on selected topics
    • Woess, W.: Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 (1994), 1-60.
    • (1994) Bull. London Math. Soc. , vol.26 , pp. 1-60
    • Woess, W.1
  • 38
    • 0010722686 scopus 로고
    • Discrete potentials on infinite networks
    • Yamasaki, M.: Discrete potentials on infinite networks, Mem. Fac. Sci., Shimane Univ., 13 (1979), 31-44.
    • (1979) Mem. Fac. Sci., Shimane Univ. , vol.13 , pp. 31-44
    • Yamasaki, M.1


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