## 2007.106: Complex cobordism classes of homogeneous spaces

2007.106:
Victor M Buchstaber and Svjetlana Terzić
(2007)
*Complex cobordism classes of homogeneous spaces.*

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 228 Kb |

## Abstract

We consider compact homogeneous spaces $G/H$ of positive Euler characteristic endowed with an invariant almost complex structure $J$ and the canonical action $\theta$ of the maximal torus $T ^{k}$ on $G/H$. We obtain explicit formula for the cobordism class of such manifold through the weights of the action $\theta$ at the identity fixed point $eH$ by an action of the quotient group $W_G/W_H$ of the Weyl groups for $G$ and $H$. In this way we show that the cobordism class for such manifolds can be computed explicitly without information on their cohomology. We also show that formula for cobordism class provides an explicit way for computing the classical Chern numbers for $(G/H, J)$. As a consequence we obtain that the Chern numbers for $(G/H, J)$ can be computed without information on cohomology for $G/H$. As an application we provide an explicit formula for cobordism classes and characteristic numbers of the flag manifolds $U(n)/T^n$, Grassmann manifolds $G_{n,k}=U(n)/(U(k)\times U(n-k))$ and some particular interesting examples. This paper is going to have continuation in which will be considered the stable complex structures equivariant under given torus action on homogeneous spaces of positive Euler characteristic.

Item Type: | MIMS Preprint |
---|---|

Subjects: | MSC 2000 > 22 Topological groups, Lie groups MSC 2000 > 57 Manifolds and cell complexes |

MIMS number: | 2007.106 |

Deposited By: | Dr Jelena Grbic |

Deposited On: | 25 August 2007 |

### Available Versions of this Item

- Complex cobordism classes of homogeneous spaces (deposited 05 September 2007)
- Complex cobordism classes of homogeneous spaces (deposited 25 August 2007)
**[Currently Displayed]**

- Complex cobordism classes of homogeneous spaces (deposited 25 August 2007)

Download Statistics: last 4 weeks

Repository Staff Only: edit this item