Supergeometry in equivariant cohomology

  • Armen Nersessian
Superspace Approach To Supersymmetry
Part of the Lecture Notes in Physics book series (LNP, volume 524)


We analyze S 1 equivariant cohomology from the supergeometrical point of view. For this purpose we equip the external algebra of given manifold with equivariant even super(pre)symplectic structure, and show, that its Poincare-Cartan invariant defines equivariant Euler classes of surfaces. This allows to derive localization formulae by use of superanalog of Stockes theorem.


Symplectic Manifold Symplectic Structure Equivariant Cohomology Exterior Algebra Localization Formula 
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  1. 1.
    A.J. Niemi, O. Tirkkonen, Ann. Phys. 235(1994), 318zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    J.J. Duistermaat, G.H. Heckman, Inv. Math. 69(1982) 259zbMATHCrossRefADSMathSciNetGoogle Scholar
  3. 2a.
  4. 3.
    M.F. Atiah, R. Bott, Topology, 23 (1984), 1CrossRefMathSciNetGoogle Scholar
  5. 4.
    N. Berline, E. Getzler, M. Vergne, Heat Kernel and Dirac Operators (Springer Verlag, Berlin, 1991)Google Scholar
  6. 5.
    E. Witten, J.Geom.Phys., 9(1992), 303 L.C.Jefferey, F.C. Kirwan, alg-geom/9307001zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. 6.
    M.F. Atiah, L. Jefferey, J.Geom.Phys., 7(1990), 119CrossRefMathSciNetADSGoogle Scholar
  8. 6a.
    M. Blau, F. Hussain, G. Tompson, Nucl.Phys. B488(1997), 541CrossRefADSGoogle Scholar
  9. 7.
    A. Schwarz, O. Zaboronsky, Comm. Math. Phys. 183(1996), 463CrossRefADSMathSciNetGoogle Scholar
  10. 8.
    O.M. Khudaverdian, A.S. Schwarz, Yu.S. Tyupkin, Lett.Math.Phys. 5(1981), 517zbMATHCrossRefMathSciNetADSGoogle Scholar
  11. 9.
    I.A. Batalin, G.A. Vilkovisky, Phys.Lett. B102(1981), 27; Phys.Rev. D28(1983) 2563; Nucl.Phys.B234(1984), 106ADSMathSciNetGoogle Scholar
  12. 10.
    A. Schwarz, Comm. Math. Phys., 155(1993), 249zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 10a.
    ibid., 158(1993), 373 O.M.Khudaverdian, dg-ga/9706004, Comm.Math.Phys.(1998) (in press)CrossRefADSMathSciNetGoogle Scholar
  14. 11.
    I.A. Batalin, R. Marnelius, Phys.Lett. B434(1998), 312; hep-th/9809208ADSMathSciNetGoogle Scholar
  15. 12.
    A. Nersessian, JETP Lett. 58, No. 1 (1993), 66 (hep-th/9305181)ADSMathSciNetGoogle Scholar
  16. 13.
    A.Nersessian, NATO ASI Series B:Physics, 331, 353 (hep-th/9306111); hep-th/9310013Google Scholar
  17. 14.
    A.J.Niemi, K.Palo, hep-th/940668Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Armen Nersessian
    • 1
    • 2
  1. 1.Bogolyubov Laboratory of Theoretical Physics, JINRDubnaRussia
  2. 2.Department of Theoretical PhysicsYerevan State UniversityYerevanArmenia

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