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Abstract
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Define Mn to be the set of
equivariant, unoriented cobordism classes of n-dimensional 2-torus manifolds, where
any such manifold is smooth, closed and n-dimensional, and has an effective
smooth action of a rank n 2-torus group (Z2)n. Then Mn forms an abelian
group with respect to disjoint union. For n = 3, we determine the group
structure of Mn and show that each class of Mn contains a small cover as its
representative.
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Keywords
2-torus manifolds, cobordism, small
cover
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Mathematical Subject Classification
Primary: 55N22, 57R85, 57S17
Secondary: 05C10, 57M60
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Milestones
Received: 7 September 2008
Revised: 27 March 2009
Accepted: 11 April 2009
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