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Equivariant cobordism of flag varieties and of symmetric varieties

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Abstract

We obtain an explicit presentation for the equivariant cobordism ring of a complete flag variety. An immediate corollary is a Borel presentation for the ordinary cobordism ring. Another application is an equivariant Schubert calculus in cobordism. We also describe the rational equivariant cobordism rings of wonderful symmetric varieties of minimal rank.

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Author information

Authors and Affiliations

  1. National Research University, Higher School of Economics, Vavilova st. 7, Moscow, 117312, Russia

    Valentina Kiritchenko

  2. Institute for Information, Transmission Problems, B. Karetnyi per. 19, Moscow, 127994, Russia

    Valentina Kiritchenko

  3. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India

    Amalendu Krishna

Authors
  1. Valentina Kiritchenko
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  2. Amalendu Krishna
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Corresponding author

Correspondence to Valentina Kiritchenko.

Additional information

The first author was supported by Dynasty Foundation, AG Laboratory NRU HSE, MESRF grants ag. 11.G34.31.0023, MK-983.2013.1, RFBR grants 12-01-31429-mol-a, 12-01-33101-mol-a-ved, 10-01-00540-a, RFBR-CNRS grant 10-01-93110-a. This study was carried out within The National Research University Higher School of Economics Academic Fund Program in 2013–2014, research grant no. 12-01-0194.

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Kiritchenko, V., Krishna, A. Equivariant cobordism of flag varieties and of symmetric varieties. Transformation Groups 18, 391–413 (2013). https://doi.org/10.1007/s00031-013-9223-z

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