Abstract
Let $M$ be an almost complex manifold and $g$ a periodic automorphism of $M$ of order $p$. Then the rotation angles of $g$ around fixed points of $g$ are naturally defined by the almost complex structure of $M$. In this paper, under the assumption that the fixed points of $g^k$ $(1\leq k\leq p-1)$ are isolated, a calculation formula is provided for the homomorphism $I_D: {\Bbb Z}_p \to {\Bbb R}/{\Bbb Z}$ defined in [8]. The formula gives a new method to study the periodic automorphisms of almost complex manifolds. As examples of the application of the formula, we show the nonexistence of the ${\Bbb Z}_p$-action of specific isotropy orders and examine whether specific rotation angles exist or not.
Citation
Kenji TSUBOI. "The finite group action and the equivariant determinant of elliptic operators II." J. Math. Soc. Japan 65 (3) 797 - 827, July, 2013. https://doi.org/10.2969/jmsj/06530797
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