RIGIDITY OF PERIODIC DIFFEOMORPHISMS OF HOMOTOPY K3 SURFACES

DOI10.1093/QMATH/HAM033zbMATH Open1140.14315arXivmath/0608703OpenAlexW2085730413MaRDI QIDQ3516847

Jin Hong Kim

Publication date: 11 August 2008

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Abstract: The aim of this paper is to show the rigidity of homologically trivial actions of prime order on K3 surfaces. To be precise, we show that homotopy K3 surfaces do not admit a periodic diffeomorphism of odd prime order 3 acting trivially on cohomology. Moreover, we give an obstruction in terms of the rationality and sign of the spin numbers to the existence of a periodic diffeomorphism of odd prime order acting trivially on cohomology of homotopy K3 surfaces.

Full work available at URL: https://arxiv.org/abs/math/0608703

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) (14J80) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

Related Items (2)

Periodic diffeomorphisms on homotopy \(E(4)\) surfaces ⋮ Periodic homeomorphisms on $S^3$ and cubes with torus knotted holes

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