On Z3-Actions on Spin 4-Manifolds

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2 k（-E8）⊕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 smo...

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Bibliographic Details
Published in:数学年刊：B辑英文版 2017 (6), p.1303-1310
Main Author: Ximin LIU Changtao XUE
Format: Article
Language:English
Online Access:Get full text
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Summary:Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2 k（-E8）⊕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.
ISSN:0252-9599
1860-6261