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

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 ≤ k ≤ p−1) are isolated, a calculation formula is provided for the homomorphism I_D: ℤ_p → ℝ/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 ℤ_p-action of specific isotropy orders and examine whether specific rotation angles exist or not.