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

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

2011-03-31

arxiv.org/abs/1103.6173v1

Mathematics

Algebraic Topology

7 pages

Scientific paper

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 set. In this paper we show that $M$ bounds equivariantly if and only if the equivariant Chern numbers $< (c_1^{T^n})^i(c_2^{T^n})^j, [M]>=0$ 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 $\lceil{n\over2}\rceil+1$.

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