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Super Characteristic Classes and Riemann-Roch Type Formula

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DOI: 10.4236/apm.2015.56034    2,595 Downloads   3,020 Views   Citations

ABSTRACT

The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the helicity group and cohomology with respect to coefficient of the helicity group. As an application, we propose the examples of Gauss-Bonnet type formula.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Taniguchi, T. (2015) Super Characteristic Classes and Riemann-Roch Type Formula. Advances in Pure Mathematics, 5, 353-366. doi: 10.4236/apm.2015.56034.

References

[1] Taniguchi, T. (2009) ADHM Construction of Super Yang-Mills Instantons. Journal of Geometry and Physics, 59, 1199-1209.
http://dx.doi.org/10.1016/j.geomphys.2009.06.003
[2] Bartocci, C., Bruzzo, U. and Ruipérez, D.H. (1991) The Geometry of Supermanifolds. Mathematics and Its Applications, Volume 71, Kluwer Academic Publishers, Norwell.
[3] LeBrun, C., Poon, Y.S. and Wells Jr., R.O. (1990) Projective Embedding of Complex Supermanifolds. Communications in Mathematical Physics, 126, 433-452.
http://dx.doi.org/10.1007/BF02125694
[4] Leites, D.A. (1980) Introduction to the Theory of Supermanifolds. Russian Mathematical Surveys, 35, 1-64.
[5] Manin, Yu.I. (1997) Gauge Field Theory and Complex Geometry. 2nd Edition, Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-07386-5
[6] Rogers, A. (2007) Supermanifolds Theory and Applications. World Scientific, Singapore City.
http://dx.doi.org/10.1142/9789812708854
[7] LeBrun, C. and Rothstein, M. (1988) Moduli of Super Riemann Surfaces. Communications in Mathematical Physics, 117, 159-176. http://dx.doi.org/10.1007/BF01228415
[8] Penkov, I.B. (1983) D-Modules on Supermanifolds. Inventiones Mathematicae, 71, 501-512.
http://dx.doi.org/10.1007/BF02095989
[9] Bartocci, C. and Bruzzo, U. (1988) Cohomology of the Structure Sheaf of Real and Complex Supermanifolds. Journal of Mathematical Physics, 29, 1789-1794.
http://dx.doi.org/10.1007/BF02095989
[10] Bott, R. and Tu, L.W. (1982) Differential Forms in Algebraic Topology. Springer, Berlin.
http://dx.doi.org/10.1007/978-1-4757-3951-0
[11] Bruzzo, U. and Ruipérez, D.H. (1989) Characteristic Classes of Super Vector Bundles. Journal of Mathematical Physics, 30, 1233-1237.
http://dx.doi.org/10.1063/1.528606
[12] Hartshorne, R. (1977) Algebraic Geometry. Springer, Berlin.
http://dx.doi.org/10.1007/978-1-4757-3849-0
[13] Hirzebruch, F. (1966) Topological Methods in Algebraic Geometry. Springer-Verlag, Berlin.
[14] Lawson Jr., H.B. and Michelsohn, M. (1989) Spin Geometry. Princeton University Press, Princeton.
[15] Voronov, A.A. and Manin, Y.I. (1990) Elements of Supergeometry. Journal of Mathematical Sciences, 51, 2069-2083.
[16] Bruzzo, U. and Fucito, F. (2004) Superlocalization Formulas and Supersymmetric Yang-Mills Theories. Nuclear Physics B, 678, 638-655.
http://dx.doi.org/10.1016/j.nuclphysb.2003.11.033
[17] Ninnemann, H. (1992) Deformations of Super Riemann Surfaces. Communications in Mathematical Physics, 150, 267-288.
http://dx.doi.org/10.1007/BF02096661
[18] Rosly, A.A., Schwarz, A.S. and Voronov, A.A. (1988) Geometry of Superconformal Manifolds. Communications in Mathematical Physics, 119, 129-152.
http://dx.doi.org/10.1007/BF01218264
[19] Crane, L. and Rabin, J.M. (1988) Super Riemann Surfaces: Uniformization and Teichmüller Theory. Communications in Mathematical Physics, 113, 601-623.
http://dx.doi.org/10.1007/BF01223239
[20] Manin, Y.I. (1991) Topics in Non-Commutative Geometry. M. B. Porter Lectures at Rice University, Houston.
http://dx.doi.org/10.1515/9781400862511
[21] Giddings, S.B. and Nelson, P. (1988) The Geometry of Super Riemann Surfaces. Communications in Mathematical Physics, 116, 607-634.
http://dx.doi.org/10.1007/BF01224903
[22] Giddings, S.B. and Nelson, P. (1988) Line Bundles on Super Riemann Surfaces. Communications in Mathematical Physics, 118, 289-302.
http://dx.doi.org/10.1007/BF01218581
[23] De Witt, B. (1992) Supermanifolds. 2nd Edition, Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511564000

  
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