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Algebraic cobordism of bundles on varieties. (English) Zbl 1348.14107

This paper considers a notion of algebraic cobordism for vector bundles on varieties, arising from the double point relation. The authors show this theory to be an extension by scalars of the standard algebraic cobordism. Additionally, they exhibit combinatorial \(\mathbb{Q}\)-bases of the cobordism groups associated with the former theory.

MSC:

14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
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References:

[1] Bryan, J., Pandharipande, R.: Local Gromov-Witten theory of curves. J. Amer. Math. Soc. 21, 101-136 (2008) · Zbl 1126.14062 · doi:10.1090/S0894-0347-06-00545-5
[2] Deshpande, D.: Algebraic cobordism of classifying spaces. arXiv:0907.4437
[3] Göttsche, L.: A conjectural generating function for numbers of curves on surfaces. Comm. Math. Phys. 196, 523-533 (1998) · Zbl 0934.14038 · doi:10.1007/s002200050434
[4] Lazard, M.: Sur les groupes de Lie formels ‘a un param‘etre. Bull. Soc. Math. France 83, 251- 274 (1955) · Zbl 0068.25703
[5] Lee, Y.-P., Lin, H.-W., Wang, C.-L.: in preparation 1101
[6] Levine, M., Morel, F.: Algebraic Cobordism. Springer Monogr. Math., Springer, Berlin (2007) · Zbl 1188.14015 · doi:10.1007/3-540-36824-8
[7] Levine, M., Pandharipande, R.: Algebraic cobordism revisited. Invent. Math. 176, 63-130 (2009) · Zbl 1210.14025 · doi:10.1007/s00222-008-0160-8
[8] Heller, J., Malagon-Lopez, J.: in preparation
[9] Maulik, D., Nekrasov, N., Okounkov, A., Pandharipande, R.: Gromov-Witten theory and Donaldson-Thomas theory I. Compos. Math. 142, 1263-1285 (2006) · Zbl 1108.14046 · doi:10.1112/S0010437X06002302
[10] Maulik, D., Nekrasov, N., Okounkov, A., Pandharipande, R.: Gromov-Witten theory and Donaldson-Thomas theory II. Compos. Math. 142, 1286-1304 (2006) · Zbl 1108.14047 · doi:10.1112/S0010437X06002314
[11] Stong, R.: Notes on Cobordism Theory. Princeton Univ. Press, Princeton, NJ (1968) · Zbl 0181.26604
[12] Totaro, B.: The Chow ring of a classifying space. In: Algebraic K-theory (Seattle, 1997), Proc. Sympos. Pure Math. 67, Amer. Math. Soc., 249-281 (1999) · Zbl 0967.14005
[13] Tzeng, Y.: Stanford thesis (2010)
[14] Yagita, N.: Applications of Atiyah-Hirzebruch spectral sequences for motivic cobordism. Proc. London Math. Soc. 90, 783-816 (2005) · Zbl 1086.55005 · doi:10.1112/S0024611504015084
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