Toral actions on 4-manifolds and their classifications

Kim, M. Ho

doi:10.1090/S0002-9947-1993-1052907-3

Toral actions on $4$-manifolds and their classifications
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Trans. Amer. Math. Soc. 335 (1993), 105-130 Request permission

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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