메뉴 건너뛰기




Volumn 16, Issue 9, 2007, Pages 1121-1163

State sum construction of two-dimensional open-closed topological quantum field theories

Author keywords

2 dimensional extended TQFT; Frobenius algebra; Open closed TQFT; Pachner move; State sum

Indexed keywords


EID: 36849091314     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216507005725     Document Type: Article
Times cited : (40)

References (34)
  • 1
    • 0030496076 scopus 로고    scopus 로고
    • Two-dimensional topological quantum field theories and Frobenius algebras
    • L. Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory Ramification 5(5) (1996) 569-587.
    • (1996) J. Knot Theory Ramification , vol.5 , Issue.5 , pp. 569-587
    • Abrams, L.1
  • 2
    • 36849058503 scopus 로고    scopus 로고
    • A note on strongly separable algebras
    • M. Aguiar, A note on strongly separable algebras, Bol. Acad. Nac. Cienc. 65 (2000) 51-60.
    • (2000) Bol. Acad. Nac. Cienc , vol.65 , pp. 51-60
    • Aguiar, M.1
  • 3
    • 36849052710 scopus 로고    scopus 로고
    • Noncommutative two-dimensional Topological Field Theories and Hurwitz numbers for real algebraic curves, to appear in Sel. Math
    • Preprint, math.GT/0202164
    • A. Alexeevski and S. M. Natanzon, Noncommutative two-dimensional Topological Field Theories and Hurwitz numbers for real algebraic curves, to appear in Sel. Math. (2006). Preprint, math.GT/0202164.
    • (2006)
    • Alexeevski, A.1    Natanzon, S.M.2
  • 4
    • 51649148614 scopus 로고
    • Topological quantum field theories
    • M. F. Atiyah, Topological quantum field theories, IHES Publ. Math. 68 (1988) 175-186.
    • (1988) IHES Publ. Math , vol.68 , pp. 175-186
    • Atiyah, M.F.1
  • 5
    • 33845324144 scopus 로고    scopus 로고
    • The topology of the category of open and closed strings
    • Recent Developments in Algebraic Topology, American Mathematical Society, Providence, RI
    • N. A. Baas, R. L. Cohen and A. Ramírez, The topology of the category of open and closed strings, in Recent Developments in Algebraic Topology, Contemporary Mathematics, Vol. 407 (American Mathematical Society, Providence, RI, 2006), pp. 11-26.
    • (2006) Contemporary Mathematics , vol.407 , pp. 11-26
    • Baas, N.A.1    Cohen, R.L.2    Ramírez, A.3
  • 6
    • 21444457888 scopus 로고    scopus 로고
    • Invariants of piecewise-linear 3-manifolds
    • J. W. Barrett and B. W. Westbury, Invariants of piecewise-linear 3-manifolds, Trans. Amer. Math. Soc. 348(10) (1996) 3997-4022.
    • (1996) Trans. Amer. Math. Soc , vol.348 , Issue.10 , pp. 3997-4022
    • Barrett, J.W.1    Westbury, B.W.2
  • 7
    • 0033541888 scopus 로고    scopus 로고
    • Spherical categories
    • J. W. Barrett and B. W. Westbury, Spherical categories, Adv. Math. 143 (1999) 357-375.
    • (1999) Adv. Math , vol.143 , pp. 357-375
    • Barrett, J.W.1    Westbury, B.W.2
  • 9
    • 0000747087 scopus 로고
    • Bulk and boundary operators in conformal field theory
    • J. L. Cardy and D. C. Lewellen, Bulk and boundary operators in conformal field theory, Phys. Lett. B 259(3) (1991) 274-278.
    • (1991) Phys. Lett. B , vol.259 , Issue.3 , pp. 274-278
    • Cardy, J.L.1    Lewellen, D.C.2
  • 10
    • 21844501619 scopus 로고
    • Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases
    • L. Crane and I. B. Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35(10) (1994) 5136-5154.
    • (1994) J. Math. Phys , vol.35 , Issue.10 , pp. 5136-5154
    • Crane, L.1    Frenkel, I.B.2
  • 11
    • 0033454552 scopus 로고    scopus 로고
    • On algebraic structures implicit in topological quantum field theory
    • L. Crane and D. N. Yetter, On algebraic structures implicit in topological quantum field theory, J. Knot Theory Ramification 8(2) (1999) 125-163.
    • (1999) J. Knot Theory Ramification , vol.8 , Issue.2 , pp. 125-163
    • Crane, L.1    Yetter, D.N.2
  • 13
    • 0037060902 scopus 로고    scopus 로고
    • Conformal correlation functions, Frobenius algebras and triangulations
    • J. Fuchs, I. Runkel and Ch. Schweigert, Conformal correlation functions, Frobenius algebras and triangulations, Nucl. Phys. B 624 (2002) 452-468.
    • (2002) Nucl. Phys. B , vol.624 , pp. 452-468
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 14
    • 0346643679 scopus 로고    scopus 로고
    • Category theory for conformal boundary conditions
    • J. Fuchs and Ch. Schweigert, Category theory for conformal boundary conditions, Fields Inst. Comm. 39 (2003) 25-71.
    • (2003) Fields Inst. Comm , vol.39 , pp. 25-71
    • Fuchs, J.1    Schweigert, C.2
  • 15
    • 21344482750 scopus 로고
    • Lattice topological field theory in two dimensions
    • M. Fukuma, S. Hosono and H. Kawai, Lattice topological field theory in two dimensions, Commun. Math. Phys. 161(1) (1994) 157-175.
    • (1994) Commun. Math. Phys , vol.161 , Issue.1 , pp. 157-175
    • Fukuma, M.1    Hosono, S.2    Kawai, H.3
  • 16
    • 44949283969 scopus 로고
    • The geometry of tensor calculus. I
    • A. Joyal and R. Street, The geometry of tensor calculus. I, Adv. Math. 88(1) (1991) 55-112.
    • (1991) Adv. Math , vol.88 , Issue.1 , pp. 55-112
    • Joyal, A.1    Street, R.2
  • 17
    • 36849012354 scopus 로고    scopus 로고
    • Towards an algebraic characterization of 3-dimensional cobordisms
    • Diagrammatic Morphisms and Applications, eds. D. E. Radford, F. J. O. Souza and D. N. Yetter, American Mathematical Society, Providence
    • T. Kerler, Towards an algebraic characterization of 3-dimensional cobordisms, in Diagrammatic Morphisms and Applications, eds. D. E. Radford, F. J. O. Souza and D. N. Yetter, Contemporary Mathematics, Vol. 318 (American Mathematical Society, Providence, 2003), pp. 141-173.
    • (2003) Contemporary Mathematics , vol.318 , pp. 141-173
    • Kerler, T.1
  • 19
    • 0002309779 scopus 로고
    • Involutory Hopf algebras and 3-manifold invariants
    • G. Kuperberg, Involutory Hopf algebras and 3-manifold invariants, Int. J. Math. 2(1) (1991) 41-66.
    • (1991) Int. J. Math , vol.2 , Issue.1 , pp. 41-66
    • Kuperberg, G.1
  • 20
    • 33745384265 scopus 로고    scopus 로고
    • Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras, preprint
    • math.AT/0510664
    • A. D. Lauda and H. Pfeiffer, Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras, preprint (2005), math.AT/0510664.
    • Lauda, A.D.1    Pfeiffer, H.2
  • 21
    • 0001260978 scopus 로고
    • Sewing constraints for conformal field theories on surfaces with boundaries
    • D. C. Lewellen, Sewing constraints for conformal field theories on surfaces with boundaries, Nucl. Phys. B 372(3) (1992) 654-682.
    • (1992) Nucl. Phys. B , vol.372 , Issue.3 , pp. 654-682
    • Lewellen, D.C.1
  • 22
    • 0035844777 scopus 로고    scopus 로고
    • On the structure of open-closed topological field theory in two dimensions
    • C. I. Lazaroiu, On the structure of open-closed topological field theory in two dimensions, Nucl. Phys. B 603(3) (2001) 497-530.
    • (2001) Nucl. Phys. B , vol.603 , Issue.3 , pp. 497-530
    • Lazaroiu, C.I.1
  • 23
    • 0003146836 scopus 로고
    • Natural associativity and commutativity
    • S. MacLane, Natural associativity and commutativity, Rice Univ. Studies 49(4) (1963) 28-46.
    • (1963) Rice Univ. Studies , vol.49 , Issue.4 , pp. 28-46
    • MacLane, S.1
  • 24
    • 36849088863 scopus 로고    scopus 로고
    • G. Moore and G. B. Segal, Lectures on Brunes, K-theory and RR Charges, Lecture notes from the Clay Institute School on Geometry and String Theory held at the Isaac Newton Institute, Cambridge, UK, available at http://www.physics.rutgers.edu/~gmoore/clay1/clay1.html, and from the ITP Miniprogram The Duality Workshop at Santa Barbara available at http://online.itp.ucsb.edu/online/mp01/moore1/(2001-2002).
    • G. Moore and G. B. Segal, Lectures on Brunes, K-theory and RR Charges, Lecture notes from the Clay Institute School on Geometry and String Theory held at the Isaac Newton Institute, Cambridge, UK, available at http://www.physics.rutgers.edu/~gmoore/clay1/clay1.html, and from the ITP Miniprogram "The Duality Workshop" at Santa Barbara available at http://online.itp.ucsb.edu/online/mp01/moore1/(2001-2002).
  • 25
    • 36849061935 scopus 로고    scopus 로고
    • 2d and 3d TQFTs and higher-dimensional algebra
    • Potsdam, Germany. Available at
    • J. Morton, 2d and 3d TQFTs and higher-dimensional algebra, poster at the conference Loops '05, Potsdam, Germany. Available at http://math.ucr.edu/ ~morton/FHKposter.ps (2005).
    • (2005) poster at the conference Loops '05
    • Morton, J.1
  • 26
    • 85025529248 scopus 로고
    • PL homeomorphic manifolds are equivalent by elementary shellings
    • U. Pachner, PL homeomorphic manifolds are equivalent by elementary shellings, Europ. J. Combin. 12 (1991) 129-145.
    • (1991) Europ. J. Combin , vol.12 , pp. 129-145
    • Pachner, U.1
  • 28
    • 84896391582 scopus 로고    scopus 로고
    • A. A. Ranicki ed, Kluwer Academic Publishers, Dordrecht
    • A. A. Ranicki (ed.), The Hauptvermutung Book, K-Monographs in Mathematics, Vol. 1 (Kluwer Academic Publishers, Dordrecht, 1996).
    • (1996) The Hauptvermutung Book, K-Monographs in Mathematics , vol.1
  • 30
    • 52049109321 scopus 로고    scopus 로고
    • Topological and conformal field theory as Frobenius algebras, preprint
    • math.CT/0512076
    • I. Runkel, J. Fjelstad, J. Fuchs and Ch. Schweigert, Topological and conformal field theory as Frobenius algebras, preprint (2005), math.CT/0512076.
    • Runkel, I.1    Fjelstad, J.2    Fuchs, J.3    Schweigert, C.4
  • 31
    • 21844511781 scopus 로고
    • Direct sum decompositions and indecomposable TQFTs
    • S. F. Sawin, Direct sum decompositions and indecomposable TQFTs, J. Math. Phys. 36(12) (1995) 6673-6680.
    • (1995) J. Math. Phys , vol.36 , Issue.12 , pp. 6673-6680
    • Sawin, S.F.1
  • 32
    • 36849043929 scopus 로고
    • Low-dimensional topology and higher-order categories I
    • Dalhousie University, Halifax, Canada, available at
    • R. Street, Low-dimensional topology and higher-order categories I, Canadian Mathematical Society Annual Seminar, Dalhousie University, Halifax, Canada, available at http://www.maths.mq.edu.au/~street/LowDTop.pdf (1995).
    • (1995) Canadian Mathematical Society Annual Seminar
    • Street, R.1
  • 33
    • 44049114062 scopus 로고
    • State sum invariants of 3-manifolds and quantum 6j-symbols
    • V. G. Turaev and O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31(4) (1992) 865-902.
    • (1992) Topology , vol.31 , Issue.4 , pp. 865-902
    • Turaev, V.G.1    Viro, O.Y.2
  • 34
    • 0001750410 scopus 로고    scopus 로고
    • Portrait of the handle as a Hopf algebra
    • Geometry and Physics, eds. J. E. Andersen, J. Dupont et al, Marcel Dekker, New York
    • D. N. Yetter, Portrait of the handle as a Hopf algebra, in Geometry and Physics, eds. J. E. Andersen, J. Dupont et al., Lecture Notes in Pure and Applied Mathematics, Vol. 184 (Marcel Dekker, New York, 1997), pp. 481-502.
    • (1997) Lecture Notes in Pure and Applied Mathematics , vol.184 , pp. 481-502
    • Yetter, D.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.