A New Cohomology Theory of Orbifold
Article
First Online:
Received:
Accepted:
- 437 Downloads
- 105 Citations
Abstract
Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.
Keywords
String Theory Theory Model Cohomology Ring Cohomology Theory String Theory Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Baily, Jr., W.: The decomposition theorem for V-manifolds. Am. J. Math. 78, 862–888 (1956)MATHGoogle Scholar
- 2.Borcea, C.: K3-surfaces with involution and mirror pairs of Calabi-Yau manifolds. In: Mirror Symmetry II. Geene, B., Yau, S.-T.(eds)., Providence, RI: Am. Math. Soc. 2001, pp. 717–743Google Scholar
- 3.Batyrev, V.V., Dais, D.: Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Topology 35, 901–929 (1996)CrossRefMathSciNetMATHGoogle Scholar
- 4.Bott, R., Tu, L. W.: Differential Forms in Algebraic Topology. GTM 82, 1982Google Scholar
- 5.Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. In: Problems in Analysis, A symposium in honour of Bochner, Princeton, N.J.: Princeton University Press, 1970, pp. 195–199Google Scholar
- 6.Chen, W., Ruan, Y.: Orbifold Gromov-Witten theory. Cont. Math. 310, 25–86 (2002)MATHGoogle Scholar
- 7.Dixon, L., Harvey, J., Vafa, C., Witten, E.: Strings on orbifolds. Nucl.Phys. B261, 651 (1985)Google Scholar
- 8.Goresky, M., MacPherson, R.: Intersection homology theory. Topology 19, 135–162 (1980)CrossRefMathSciNetMATHGoogle Scholar
- 9.Kawasaki, T.: The signature theorem for V-manifolds. Topology 17, 75–83 (1978)CrossRefMATHGoogle Scholar
- 10.Kawasaki, T.: The Riemann-Roch theorem for complex V-manifolds. Osaka J. Math. 16, 151–159 (1979)MathSciNetMATHGoogle Scholar
- 11.Li, An-Min., Ruan, Y.: Symplectic surgery and GW-invariants of Calabi-Yau 3-folds. Invent. Math. 145(1), 151–218 (2001)CrossRefGoogle Scholar
- 12.Reid, M.: McKay correspondence. Seminarire BOurbaki, Vol. 1999/2000. Asterisque No. 176, 53–72 (2002)Google Scholar
- 13.Roan, S.: Orbifold Euler characteristic. Mirror symmetry, II, AMS/IP Stud. Adv. Math. 1, Providence, RI: Am. Math. Soc., , 1997, pp. 129–140Google Scholar
- 14.Ruan, Y.: Surgery, quantum cohomology and birational geometry. Am. Math.Soc.Trans (2), 196, 183–198 (1999)Google Scholar
- 15.Satake, I.: The Gauss-Bonnet theorem for V-manifolds. J. Math. Soc. Japan 9, 464–492 (1957)MATHGoogle Scholar
- 16.Scott, P.: The geometries of 3-manifolds. Bull. London. Math. Soc. 15, 401–487 (1983)MathSciNetMATHGoogle Scholar
- 17.Thurston, W.: The Geometry and Topology of Three-Manifolds. Princeton Lecture Notes, 1979Google Scholar
- 18.Voisin, C.: Miroirs et involutions sur les surfaces K3. In: Journées de géométrie algébrique d’Orsay, juillet 92, édité par A. Beauville, O. Debarre, Y. Laszlo, Astérisque 218, 273–323 (1993)Google Scholar
- 19.Zaslow, E.: Topological orbifold models and quantum cohomology rings. Commun. Math. Phys. 156(2), 301–331 (1993)MATHGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2004