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On ℤ3-actions on spin 4-manifolds

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Abstract

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2k(−E s ) ⊕ lH, where H is the hyperbolic form. In this paper, the authors prove that if there exists a locally linear pseudofree ℤ3-action on X, then Sign(g,X) ≡ −k mod 3. They also investigate the smoothability of locally linear ℤ3-action satisfying above congruence. In particular, it is proved that there exist some nonsmoothable locally linear ℤ3-actions on certain elliptic surfaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Ximin Liu

  2. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, Hebei, China

    Changtao Xue

Authors
  1. Ximin Liu
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  2. Changtao Xue
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Correspondence to Ximin Liu.

Additional information

The work was supported by the National Natural Science Foundation of China (Nos. 11371076, 11431009) and the Natural Science Foundation of Hebei Province of China (No.A2014501040).

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Liu, X., Xue, C. On ℤ3-actions on spin 4-manifolds. Chin. Ann. Math. Ser. B 38, 1303–1310 (2017). https://doi.org/10.1007/s11401-017-1038-0

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  • DOI: https://doi.org/10.1007/s11401-017-1038-0

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