2-torus manifolds, cobordism and small covers

Details 2-torus manifolds, cobordism and small covers 2-torus manifolds, cobordism and small covers

2007-01-31

arxiv.org/abs/math/0701928v1

Pacific J. Math. 241 (2009), 285--308.

Mathematics

Algebraic Topology

19 pages, 4 figures

Scientific paper

Let ${\frak M}_n$ be the set of equivariant unoriented cobordism classes of all $n$-dimensional 2-torus manifolds, where an $n$-dimensional 2-torus manifold $M$ is a smooth closed manifold of dimension $n$ with effective smooth action of a rank $n$ 2-torus group $({\Bbb Z}_2)^n$. Then ${\frak M}_n$ forms an abelian group with respect to disjoint union. This paper determines the group structure of ${\frak M}_n$ and shows that each class of ${\frak M}_n$ contains a small cover as its representative in the case $n=3$.

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