Journal of the Mathematical Society of Japan

The finite group action and the equivariant determinant of elliptic operators II


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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.

Article information

J. Math. Soc. Japan, Volume 65, Number 3 (2013), 797-827.

First available in Project Euclid: 23 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58J20: Index theory and related fixed point theorems [See also 19K56, 46L80]
Secondary: 57S17: Finite transformation groups

finite group action elliptic operator almost complex manifold


TSUBOI, Kenji. The finite group action and the equivariant determinant of elliptic operators II. J. Math. Soc. Japan 65 (2013), no. 3, 797--827. doi:10.2969/jmsj/06530797.

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