메뉴 건너뛰기




Volumn 198, Issue 2 SPEC. ISS., 2005, Pages 732-846

Differential geometry of gerbes

Author keywords

3 Curvature; Connection; Gerbe; Non abelian cohomology

Indexed keywords


EID: 28744434776     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2005.06.014     Document Type: Article
Times cited : (125)

References (46)
  • 1
    • 0001272369 scopus 로고
    • On the joins of Hensel rings
    • M. Artin On the joins of Hensel rings Adv. Math. 7 1971 282-296
    • (1971) Adv. Math. , vol.7 , pp. 282-296
    • Artin, M.1
  • 2
    • 13244264886 scopus 로고    scopus 로고
    • Nonabelian bundle Gerbes, their differential geometry and gauge theory
    • P. Aschieri L. Cantini B. Jurčo Nonabelian bundle Gerbes, their differential geometry and gauge theory Comm. Math. Physics 254 2005 367-400
    • (2005) Comm. Math. Physics , vol.254 , pp. 367-400
    • Aschieri, P.1    Cantini, L.2    Jurčo, B.3
  • 4
    • 28744441548 scopus 로고    scopus 로고
    • Two-dimensional parallel transport: Combinatorics and functoriality
    • arXiv:math-ph/0105050
    • R. Attal, Two-dimensional parallel transport: Combinatorics and functoriality, arXiv:mAth-ph/0105050.
    • Attal, R.1
  • 6
    • 0000227933 scopus 로고    scopus 로고
    • Higher-dimensional algebra III: N-categories and the algebra of opetopes
    • J. Baez J. Dolan Higher-dimensional algebra III: n-categories and the algebra of opetopes Adv. Math. 135 1998 145-206
    • (1998) Adv. Math. , vol.135 , pp. 145-206
    • Baez, J.1    Dolan, J.2
  • 8
    • 0003343964 scopus 로고
    • Cohomologie Cristalline des Schémas de Caractéristique p>0
    • Springer, Berlin
    • P. Berthelot, Cohomologie Cristalline des Schémas de Caractéristique p>0, Lecture Notes in Mathematics vol. 407, Springer, Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.407
    • Berthelot, P.1
  • 10
    • 0001434515 scopus 로고
    • Théorie de Schreier supérieure
    • L. Breen Théorie de Schreier supérieure Ann. Sci. Éc. Norm. Sup. 25 4 1992 465-514
    • (1992) Ann. Sci. Éc. Norm. Sup. , vol.25 , Issue.4 , pp. 465-514
    • Breen, L.1
  • 11
    • 0346204505 scopus 로고
    • Tannakian Categories in Motives
    • L. Breen Tannakian Categories in Motives Proc. Symp. Pure Math. 55 part 1 1994 337-376
    • (1994) Proc. Symp. Pure Math. , vol.55 , Issue.PART 1 , pp. 337-376
    • Breen, L.1
  • 12
    • 0001990148 scopus 로고
    • Classification of 2-gerbes and 2-stacks
    • Société mathématique de France
    • L. Breen, Classification of 2-gerbes and 2-stacks, Astérisque 225, Société mathématique de France, 1994.
    • (1994) Astérisque , vol.225
    • Breen, L.1
  • 13
    • 28744433833 scopus 로고    scopus 로고
    • Ensembles croisés et algèbre simpliciale, appendix B to J.-P. Labesse, Cohomologie, Stabilité et Changement de Base
    • Société mathématique de France
    • L. Breen, Ensembles croisés et algèbre simpliciale, appendix B to J.-P. Labesse, Cohomologie, Stabilité et Changement de Base, Astérisque 257, Société mathématique de France, 1999, pp. 135-161.
    • (1999) Astérisque , vol.257 , pp. 135-161
    • Breen, L.1
  • 14
    • 0035951177 scopus 로고    scopus 로고
    • Combinatorial differential forms
    • =[cdf]
    • =[cdf] L. Breen, W. Messing, Combinatorial differential forms, Advances in Math. 164 (2001) 203-282.
    • (2001) Advances in Math. , vol.164 , pp. 203-282
    • Breen, L.1    Messing, W.2
  • 15
    • 0003241840 scopus 로고
    • Loop spaces, characteristic classes and geometric quantization
    • Birkhäuser, Basel
    • J.-L. Brylinski, Loop spaces, characteristic classes and geometric quantization, Progress in Mathematics, vol. 107, Birkhäuser, Basel, 1993.
    • (1993) Progress in Mathematics , vol.107
    • Brylinski, J.-L.1
  • 16
    • 23044460259 scopus 로고    scopus 로고
    • Non-abelian Wilson Surfaces
    • arXiv:hep-th/011018
    • I. Chepelev, Non-abelian Wilson Surfaces, J. High Energy Phys. 2002 (2) 13. arXiv:hEp-th/011018.
    • (2002) J. High Energy Phys. , vol.2 , pp. 13
    • Chepelev, I.1
  • 17
    • 0002269687 scopus 로고
    • Sur la cohomologie non abélienne I (dimension deux)
    • P. Dedecker Sur la cohomologie non abélienne I (dimension deux) Canad. J. Math. 12 1960 231-251
    • (1960) Canad. J. Math. , vol.12 , pp. 231-251
    • Dedecker, P.1
  • 18
    • 0001193482 scopus 로고
    • La formule de dualité globale
    • Springer, Berlin Théorie des Topos et Cohomologie Etale des Schémas (SGA 7)
    • P. Deligne, La formule de dualité globale, in Théorie des Topos et Cohomologie Etale des Schémas (SGA 7), Lecture Notes in Mathematics, vol. 305, Springer, Berlin, 1973.
    • (1973) Lecture Notes in Mathematics , vol.305
    • Deligne, P.1
  • 19
    • 4243393559 scopus 로고
    • Schémas en groupes I: Propriétés générales des schémas en groupes, (SGA 3)
    • Springer, Berlin
    • M. Demazure, A. Grothendieck, Schémas en groupes I: Propriétés générales des schémas en groupes, (SGA 3), Lecture Notes in Mathematics, vol. 151, Springer, Berlin 1970.
    • (1970) Lecture Notes in Mathematics , vol.151
    • Demazure, M.1    Grothendieck, A.2
  • 20
    • 28744433674 scopus 로고    scopus 로고
    • The Mathematics of Fivebranes
    • talk at the ICM 1998 Extra Volume ICM
    • R. Dijkgraaf, The Mathematics of Fivebranes, talk at the ICM 1998, Documenta Math. Extra Volume ICM, 1998.
    • (1998) Documenta Math.
    • Dijkgraaf, R.1
  • 21
    • 21344482752 scopus 로고
    • Higher algebraic structures and quantization
    • D.S. Freed Higher algebraic structures and quantization Commun. Math. Phys. 159 1994 343-398
    • (1994) Commun. Math. Phys. , vol.159 , pp. 343-398
    • Freed, D.S.1
  • 22
    • 0000973888 scopus 로고    scopus 로고
    • Anomalies in string theory with D-branes
    • (version 2 available as arXiv:hep-th/9907189)
    • D.S. Freed E. Witten Anomalies in string theory with D-branes Asian J. Math. 3 1999 819-851 (version 2 available as arXiv:hEp-th/9907189)
    • (1999) Asian J. Math. , vol.3 , pp. 819-851
    • Freed, D.S.1    Witten, E.2
  • 23
    • 4043155453 scopus 로고
    • Cohomologie non abélienne
    • Springer, Berlin
    • J. Giraud, Cohomologie non abélienne, Grundlehren, vol. 179, Springer, Berlin, 1971.
    • (1971) Grundlehren , vol.179
    • Giraud, J.1
  • 24
    • 0004072042 scopus 로고    scopus 로고
    • Lectures on special lagrangian submanifolds
    • arXiv:math.DG/9907034
    • N. Hitchin, Lectures on special lagrangian submanifolds, arXiv:mAth.DG/ 9907034 (1999).
    • (1999)
    • Hitchin, N.1
  • 25
    • 0000861591 scopus 로고
    • Complexe cotangent et Déformations I,II
    • Springer, Berlin
    • L. Illusie, Complexe cotangent et Déformations I,II, Lecture Notes in Mathematics, vols. 239, 283, Springer, Berlin, 1971-1972.
    • (1971) Lecture Notes in Mathematics , vol.239 , Issue.283
    • Illusie, L.1
  • 26
    • 33645929090 scopus 로고    scopus 로고
    • Gerbes of massive type II configurations
    • J. Kalkkinen Gerbes of massive type II configurations J. High Energy Physics 9907 1999 2-22
    • (1999) J. High Energy Physics , vol.9907 , pp. 2-22
    • Kalkkinen, J.1
  • 27
    • 0002717638 scopus 로고
    • Representation theory and D-modules on flag varieties
    • Orbites Unipotentes et représentations III: Orbites et faisceaux pervers
    • M. Kashiwara Representation theory and D-modules on flag varieties, in: Orbites Unipotentes et représentations III: Orbites et faisceaux pervers Astérisque 173-174 1989 55-110
    • (1989) Astérisque , vol.173-174 , pp. 55-110
    • Kashiwara, M.1
  • 28
    • 0000789738 scopus 로고
    • Extensions centrales d'algébres de Lie
    • C. Kassel J.-L. Loday Extensions centrales d'algébres de Lie Ann. Inst. Fourier 32 1982 119-142
    • (1982) Ann. Inst. Fourier , vol.32 , pp. 119-142
    • Kassel, C.1    Loday, J.-L.2
  • 31
    • 84973941594 scopus 로고
    • Differential forms with values in groups
    • A. Kock Differential forms with values in groups Bull. Austral. Math. Soc 25 1982 357-386
    • (1982) Bull. Austral. Math. Soc , vol.25 , pp. 357-386
    • Kock, A.1
  • 32
    • 0002295861 scopus 로고    scopus 로고
    • Combinatorics of curvature, and the Bianchi identity
    • A. Kock Combinatorics of curvature, and the Bianchi identity Theory and Applications of Categories vol. 2 1996 69-89
    • (1996) Theory and Applications of Categories , vol.2 , pp. 69-89
    • Kock, A.1
  • 33
    • 84972866557 scopus 로고
    • Strongly homotopy Lie algebras
    • T. Lada M. Markl Strongly homotopy Lie algebras Comm. Algebra 23 1995 2147-2161
    • (1995) Comm. Algebra , vol.23 , pp. 2147-2161
    • Lada, T.1    Markl, M.2
  • 34
    • 0042294448 scopus 로고    scopus 로고
    • Champs algébriques
    • Springer, Berlin
    • G. Laumon, L. Moret-Bailly, Champs algébriques, Ergebnisse, vol. 39, Springer, Berlin, 2000.
    • (2000) Ergebnisse , vol.39
    • Laumon, G.1    Moret-Bailly, L.2
  • 35
    • 0037174517 scopus 로고    scopus 로고
    • Holonomy and parallel transport for abelian gerbes
    • (arXiv:math.DG/0007053)
    • M. Mackaay R. Picken Holonomy and parallel transport for abelian gerbes Adv. Math. 170 2002 287-339 (arXiv:mAth.DG/0007053)
    • (2002) Adv. Math. , vol.170 , pp. 287-339
    • Mackaay, M.1    Picken, R.2
  • 36
    • 0003356529 scopus 로고    scopus 로고
    • Categories for the working mathematician
    • second ed., Springer, Berlin
    • S. Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics, vol. 5, second ed., Springer, Berlin, 1997.
    • (1997) Graduate Texts in Mathematics , vol.5
    • Mac Lane, S.1
  • 37
    • 0010739137 scopus 로고
    • Homotopy equivalences in 2-categories
    • Groups of self-equivalences and related topics (Montreal, 1988) Springer, Berlin
    • H.Marcum, Homotopy equivalences in 2-categories, in: Groups of self-equivalences and related topics (Montreal, 1988), Lecture Notes in Mathematics, vol. 1425, Springer, Berlin, 1990, pp. 71-86.
    • (1990) Lecture Notes in Mathematics , vol.1425 , pp. 71-86
    • Marcum, H.1
  • 38
    • 0040031777 scopus 로고
    • Universal Extensions and On Dimensional Crystalline Cohomology
    • Springer, Berlin
    • B. Mazur, W. Messing, Universal Extensions and On Dimensional Crystalline Cohomology, Lecture Notes in Mathematics, vol. 370, Springer, Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.370
    • Mazur, B.1    Messing, W.2
  • 39
    • 0013069039 scopus 로고
    • The universal extensions of an abelian variety by a vector group
    • W. Messing The universal extensions of an abelian variety by a vector group Symposia Math. XI 1973 359-372
    • (1973) Symposia Math. , vol.11 , pp. 359-372
    • Messing, W.1
  • 42
    • 84878113160 scopus 로고
    • Some concepts and applications of non-abelian cohomology theory
    • Transactions of the Moscow Mathematical Society for the year 1967, American Mathematical Society, Providence, RI
    • A. Onishchik, Some concepts and applications of non-abelian cohomology theory, Transactions of the Moscow Mathematical Society for the year 1967, American Mathematical Society, Providence, RI, 1969, pp. 49-97.
    • (1969) , pp. 49-97
    • Onishchik, A.1
  • 44
    • 0000163152 scopus 로고
    • Group cohomology for Picard categories
    • K.-H. Ulbrich Group cohomology for Picard categories J. Algebra 91 1984 464-498
    • (1984) J. Algebra , vol.91 , pp. 464-498
    • Ulbrich, K.-H.1
  • 45
    • 84971791622 scopus 로고
    • On the correspondence between gerbes and bouquets
    • K.-H. Ulbrich On the correspondence between gerbes and bouquets Math. Proc. Cambridge Philos. Soc. 108 1990 1-5
    • (1990) Math. Proc. Cambridge Philos. Soc. , vol.108 , pp. 1-5
    • Ulbrich, K.-H.1
  • 46
    • 84975994900 scopus 로고
    • On cocycle bitorsors and gerbes over a Grothendieck topos
    • K.-H. Ulbrich On cocycle bitorsors and gerbes over a Grothendieck topos Math. Proc. Cambridge Philos. Soc. 110 1991 49-55
    • (1991) Math. Proc. Cambridge Philos. Soc. , vol.110 , pp. 49-55
    • Ulbrich, K.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.