Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 035, 10 pages      arXiv:0803.4168      https://doi.org/10.3842/SIGMA.2008.035

Relative differential K-characters

Mohamed Maghfoul
Université Ibn Tofaïl, Département de Mathématiques, Kénitra, Maroc

Received November 26, 2007, in final form March 17, 2008; Published online March 28, 2008

Abstract
We define a group of relative differential K-characters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the non-relative case. Some secondary geometric invariants are expressed in this theory.

Key words: geometric K-homology; differential K-characters.

pdf (223 kb)   ps (163 kb)   tex (13 kb)

References

  1. Atiyah M.F., Patodi V.K., Singer I.M., Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69.
  2. Atiyah M.F., Patodi V.K., Singer I.M., Spectral asymmetry and Riemannian geometry. II, Math. Proc. Cambridge Philos. Soc. 78 (1975), 405-432.
  3. Atiyah M.F., Patodi V.K., Singer I.M., Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976), 71-99.
  4. Asahawa T., Surgimoto S., Terashima S., D-branes, matrix theory and K-homology, J. High Energy Phys. 2002 (2002), no. 3, 034, 40 pages, hep-th/0108085.
  5. Baum P., Douglas R., K-homology and index theory, in Operator Algebras and Applications, Proc. Sympos. Pure Math., Vol. 38, Amer. Math. Soc., Providence, R.I., 1982, 117-173.
  6. Baum P., Douglas R., Relative K-homology and C*-algebras, K-theory 5 (1991), 1-46.
  7. Bunke U., Turner P., Willerton S., Gerbes and homotopy quantum field theories, Algebr. Geom. Topol. 4 (2004), 407-437.
  8. Benameur M.T., Maghfoul M., Differential characters in K-theory, Differential Geom. Appl. 24 (2006), 417-432.
  9. Brightwell M., Turner P., Relative differential characters, Comm. Anal. Geom. 14 (2006), 269-282, math.AT/0408333.
  10. Cheeger J., Simons J., Differential characters and geometric invariants, in Geometry and Topology (1983/84, College Park, Md.), Lecture Notes in Math., Vol. 1167, Springer, Berlin, 1985, 50-80.
  11. Chern S.S., Simons J., Characteristic forms and geometric invariants, Ann. of Math. (2) 79 (1974), 48-69.
  12. Harvey R., Lawson B., Lefschetz-Pontrjagin duality for differential characters, An. Acad. Brasil. Ciênc. 73 (2001), 145-159.
  13. Hopkins M.J., Singer I.M., Quadratic functions in geometry, topology and M-theory, J. Differential Geom. 70 (2005), 329-452, math.AT/0211216.
  14. Lott J., R/Z-index theory, Comm. Anal. Geom. 2 (1994), 279-311.
  15. Lupercio E., Uribe B., Differential characters on orbifolds and string connection. I. Global quotients, in Gromov-Witten Theory of Spin Curves and Orbifolds (May 3-4, 2003, San Francisco, CA, USA), Editors T.J. Jarvis et al., Amer. Math. Soc., Providence, Contemp. Math. 403 (2006), 127-142, math.DG/0311008.
  16. Periwal V., D-branes charges and K-homology, J. High Energy Phys. 2000 (2000), no. 7, 041, 6 pages, hep-th/9805170.
  17. Reis R.M., Szabo R.J., Geometric K-homology of flat D-branes, Comm. Math. Phys. 266 (2006), 71-122, hep-th/0507043.

Previous article   Next article   Contents of Volume 4 (2008)