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| On Z3-Actions on Spin 4-Manifolds |
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Citation： |
Ximin LIU,Changtao XUE.On Z3-Actions on Spin 4-Manifolds[J].Chinese Annals of Mathematics B,2017,38(6):1303~1310 |
| Page view： 1320
Net amount： 1327 |
Authors： |
Ximin LIU; Changtao XUE |
Foundation： |
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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| Abstract： |
Let $X$ be a closed, simply-connected, smooth, spin $4$-manifold
whose intersection form is isomorphic to $2k(-E_8)\oplus lH$, where
$H$ is the hyperbolic form. In this paper, the authors prove that if
there exists a locally linear pseudofree $\mathbb{Z}_3$-action on
$X$, then ${\rm Sign}(g,X)\equiv-k~{\rm mod}~3$. They also
investigate the smoothability of locally linear
$\mathbb{Z}_3$-action satisfying above congruence. In particular, it
is proved that there exist some nonsmoothable locally linear
$\mathbb{Z}_3$-actions on certain elliptic surfaces. |
Keywords： |
Group action, Locally linear, Kirby-Siebenmann invariant,
Nonsmoothable |
Classification： |
57R57, 57M60, 57S25 |
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