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# Mathematical Research Letters

## Volume 18 (2011)

### Number 6

### Equivariant Chern numbers and the number of fixed points for unitary torus manifolds

Pages: 1319 – 1325

DOI: https://dx.doi.org/10.4310/MRL.2011.v18.n6.a19

#### Authors

#### Abstract

Let $M^{2n}$ be a unitary torus $(2n)$-manifold, i.e., a $(2n)$-dimensional oriented stable complex connected closed $T^n$-manifold having a nonempty fixed point set. In this paper we show that $M$ bounds equivariantly if and only if the equivariant Chern numbers $\langle (c_1^{T^n})^i(c_2^{T^n})^j, [M]\rangle=0$ for all $i, j\in {\Bbb N}$, where $c_l^{T^n}$ denotes the $l$th equivariant Chern class of $M$. As a consequence, we also show that if $M$ does not bound equivariantly then the number of fixed points is at least $\lceil{n\over2}\rceil+1$.

Published 20 February 2012