Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Stably and almost complex structures on bounded flag manifolds


Author: Yusuf Civan
Journal: Proc. Amer. Math. Soc. 134 (2006), 1537-1548
MSC (2000): Primary 57S25, 57N65
DOI: https://doi.org/10.1090/S0002-9939-05-08085-8
Published electronically: October 18, 2005
MathSciNet review: 2199203
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring $ \Omega_*^U$.


References [Enhancements On Off] (What's this?)

  • 1. V. Batyrev, Quantum cohomology rings of toric manifolds, Astérique, Sociéte Mathématique de France, vol. 218, 1993, pp. 9-34. MR 1265307 (95b:32034)
  • 2. A. Brønsted, An Introduction to Convex Polytopes, Springer-Verlag, New York, 1983. MR 0683612 (84d:52009)
  • 3. V. Buchstaber and T. Panov, Torus Actions, Combinatorial Topology and Homological Algebra, AMS University Lecture Series, vol.24, 2002. MR 1897064 (2003e:57039)
  • 4. V. Buchstaber and N. Ray, Flag manifolds and the Landweber-Novikov algebra, Geometry and Topology, vol. 2, 1998, pp. 79-101. MR 1623426 (99c:57064)
  • 5. V. Buchstaber and N. Ray, Tangential structures on toric manifolds, and connected sums of polytopes, International Mathematical Research Notices, vol. 4, 2001, pp. 193-219. MR 1813798 (2002b:57043)
  • 6. Y. Civan, The Topology of Families of Toric Manifolds, Ph.D. Thesis, University of Manchester, 2001.
  • 7. Y. Civan, $ KO$-groups of bounded flag manifolds, Turkish Journal of Mathematics, vol. 26, 2002, pp. 447-463. MR 1944933 (2003m:55005)
  • 8. Y. Civan and N. Ray, Homotopy decompositions and real $ K$-theory of Bott towers, K-theory, vol. 34, 2005, pp. 1-33.
  • 9. M. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. Journal, vol. 62, 1991, pp. 417-451. MR 1104531 (92i:52012)
  • 10. G. Ewald, Combinatorial Convexity and Algebraic Geometry, Springer-Verlag, New York, GTM 168, 1996. MR 1418400 (97i:52012)
  • 11. T. Oda, Convex Bodies and Algebraic Geometry, Springer-Verlag, New York, 1988. MR 0922894 (88m:14038)
  • 12. N. Ray, On a construction in bordism theory, Proceedings of the Edinburgh Mathematical Society, 29, 1986, pp. 413-422.MR 0865274 (88a:57065)
  • 13. N. Ray, R. Switzer and L. Taylor, Normal structures and bordism theory with applications to $ MSp_*$, Memoires of the American Mathematical Society, vol. 193-12, 1977. MR 0461520 (57:1505)
  • 14. R.E. Stong, Notes on Cobordism Theory, Princeton University Press, New Jersey, 1968. MR 0248858 (40:2108)
  • 15. E. Thomas Complex structures on real vector bundles, American Journal of Mathematics, vol. 89, 1967, pp. 887-908. MR 0220310 (36:3375)
  • 16. J. West, Generating trees and forbidden subsequences, Discrete Mathematics, vol. 157, 1996, pp. 363-374. MR 1417303 (98d:05013)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57S25, 57N65

Retrieve articles in all journals with MSC (2000): 57S25, 57N65


Additional Information

Yusuf Civan
Affiliation: Department of Mathematics, Suleyman Demirel University, Isparta, 32260, Turkey
Email: ycivan@fef.sdu.edu.tr

DOI: https://doi.org/10.1090/S0002-9939-05-08085-8
Keywords: Bounded flag manifolds, torus actions, stably and almost complex structures
Received by editor(s): April 23, 2004
Received by editor(s) in revised form: December 16, 2004
Published electronically: October 18, 2005
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society