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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Toral actions on $ 4$-manifolds and their classifications


Author: M. Ho Kim
Journal: Trans. Amer. Math. Soc. 335 (1993), 105-130
MSC: Primary 57S25; Secondary 57N13
DOI: https://doi.org/10.1090/S0002-9947-1993-1052907-3
MathSciNet review: 1052907
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Abstract: The existence of a cross-section is proved for some nonorientable $ 4$-manifolds with a $ {T^2}$-action. Two $ 4$-manifolds with a $ {T^2}$-action, which have the same previously known invariants, are constructed. By using a new homotopy invariant, they are proved to be homotopy inequivalent. Finally a stable diffeomorphism theorem is proved.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1052907-3
Keywords: Toral action, orbit space, nonorientable, cross-section, fixed points, equivariant, stabilizers
Article copyright: © Copyright 1993 American Mathematical Society