Geodesic
Generalized Equivariant Cohomology and Stratifications
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 483-496

Voir la notice de l'article provenant de la source Cambridge University Press

For $T$ a compact torus and $E_{T}^{*}$ a generalized $T$ -equivariant cohomology theory, we provide a systematic framework for computing $E_{T}^{*}$ in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute $H_{T}^{*}\left( X \right)$ as an $H_{T}^{*}\left( pt \right)$ -module when $X$ is a direct limit of smooth complex projective ${{T}_{\mathbb{C}}}$ -varieties. We perform this computation on the affine Grassmannian of a complex semisimple group.
DOI : 10.4153/CMB-2016-032-5
Mots-clés : 55N91, 19L47, equivariant cohomology theory, stratification, affine Grassmannian 
Crooks, Peter; Holden, Tyler. Generalized Equivariant Cohomology and Stratifications. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 483-496. doi: 10.4153/CMB-2016-032-5
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[1] [1] Atiyah, M. F. and Bott, R., The Yang-Mills equations over Riemann surfaces.Philos. Trans. Roy. Soc. London. Ser. A 308(1983), no. 1505, 523–615. Google Scholar | DOI

[2] [2] Biatynicki-Birula, A.. Some theorems on actions of algebraic groups.Ann. of Math. 98(1973), 480–497. Google Scholar | DOI

[3] [3] Cole, M., C. Greenlees, J. P., and Kriz, I., The universality of equivariant complex bordism.Math. Z. 239(2002), no. 3, 455–475. Google Scholar | DOI

[4] [4] Frenkel, E. and D. Ben-Zvi, Vertex algebras and algebraic curves. Second éd.,Mathematical Surveys and Monographs, 88, American Mathematical Society, Providence, RI, 2004. Google Scholar | DOI

[5] [5] Harada, M., Henriques, A., and Holm, T. S., Computation of generalized equivariantcohomologies ofKac-Moody flag varieties. Adv. Math. 197(2005), no. 1,198-221. Google Scholar | DOI

[6] [6] Hovey, M., Palmieri, J. H., and Strickland, N. P., Axiomatic stable homotopy theory.Mem.Amer. Math.Soc. 128(1997), no. 610. Google Scholar | DOI

[7] [7] Kamnitzer, J., Mirkovic-Vilonen cycles and polytopes. Ann. of Math.(2) 171(2010), no. 1, 245–294. Google Scholar | DOI

[8] [8] Kirwan, E. C., Cohomology of quotients in symplectic and algebraic geometry. Mathematical Notes, 31, Princeton University Press, Princeton, NJ, 1984. Google Scholar | DOI

[9] [9] Magyar, P., Schubert classes of a loop group. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.523.3671 &rep=rep1 &type=pdf Google Scholar

[10] [10] May, J. P., Equivarianthomotopy and cohomology theory. CBMS Regional Conference Series in Mathematics, 91, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. Google Scholar | DOI

[11] [11] Mirkovic, I. and Vilonen, K., Geometric Langlands duality and representations of algebraic groups over commutative rings. Ann. of Math.(2) 166(2007), no. 1, 95–143. Google Scholar | DOI

[12] [12] Mitchell, S. A., Quillen's theorem on buildings and the loops on a symmetric space. Enseign.Math. (2) 34(1988), no. 1-2, 123–166. Google Scholar

[13] [13] Pressley, A. and Segal, G., Loop groups. Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1986. Google Scholar

[14] [14] Segal, G., Equivariant K-theory. Inst. Hautes Études Sci. Publ. Math. 34(1968), 129–151. Google Scholar

[15] [15] Sinha, D. P., Computations of complex equivariantbordism rings. Amer. J. Math. 123(2001), no. 4, 577–605. Google Scholar | DOI

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