Stably and almost complex structures on bounded flag manifolds

Civan, Yusuf

doi:10.1090/S0002-9939-05-08085-8

Stably and almost complex structures on bounded flag manifolds
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by Yusuf Civan

Proc. Amer. Math. Soc. 134 (2006), 1537-1548

DOI: https://doi.org/10.1090/S0002-9939-05-08085-8

Published electronically: October 18, 2005

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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

Victor V. Batyrev, Quantum cohomology rings of toric manifolds, Astérisque 218 (1993), 9–34. Journées de Géométrie Algébrique d’Orsay (Orsay, 1992). MR 1265307
Arne Brøndsted, An introduction to convex polytopes, Graduate Texts in Mathematics, vol. 90, Springer-Verlag, New York-Berlin, 1983. MR 683612, DOI 10.1007/978-1-4612-1148-8
Victor M. Buchstaber and Taras E. Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series, vol. 24, American Mathematical Society, Providence, RI, 2002. MR 1897064, DOI 10.1090/ulect/024
Victor M. Buchstaber and Nigel Ray, Flag manifolds and the Landweber-Novikov algebra, Geom. Topol. 2 (1998), 79–101. MR 1623426, DOI 10.2140/gt.1998.2.79
Victor M. Buchstaber and Nigel Ray, Tangential structures on toric manifolds, and connected sums of polytopes, Internat. Math. Res. Notices 4 (2001), 193–219. MR 1813798, DOI 10.1155/S1073792801000125
Y. Civan, The Topology of Families of Toric Manifolds, Ph.D. Thesis, University of Manchester, 2001.
Yusuf Civan, $K\rm O$-groups of bounded flag manifolds, Turkish J. Math. 26 (2002), no. 4, 447–463. MR 1944933
Y. Civan and N. Ray, Homotopy decompositions and real $K$-theory of Bott towers, K-theory, vol. 34, 2005, pp. 1–33.
Michael W. Davis and Tadeusz Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417–451. MR 1104531, DOI 10.1215/S0012-7094-91-06217-4
Günter Ewald, Combinatorial convexity and algebraic geometry, Graduate Texts in Mathematics, vol. 168, Springer-Verlag, New York, 1996. MR 1418400, DOI 10.1007/978-1-4612-4044-0
Tadao Oda, Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 15, Springer-Verlag, Berlin, 1988. An introduction to the theory of toric varieties; Translated from the Japanese. MR 922894
Nigel Ray, On a construction in bordism theory, Proc. Edinburgh Math. Soc. (2) 29 (1986), no. 3, 413–422. MR 865274, DOI 10.1017/S0013091500017855
Nigel Ray, Robert Switzer, and Larry Taylor, Normal structures and bordism theory, with applications to $M\textrm {Sp}_{^*}$, Mem. Amer. Math. Soc. 12 (1977), no. 193, ix+66. MR 461520, DOI 10.1090/memo/0193
Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
Emery Thomas, Complex structures on real vector bundles, Amer. J. Math. 89 (1967), 887–908. MR 220310, DOI 10.2307/2373409
Julian West, Generating trees and forbidden subsequences, Proceedings of the 6th Conference on Formal Power Series and Algebraic Combinatorics (New Brunswick, NJ, 1994), 1996, pp. 363–374 (English, with English and French summaries). MR 1417303, DOI 10.1016/S0012-365X(96)83023-8