Periods of holomorphic maps on compact Riemann surfaces and product of spheres

ABSTRACT

In this article, we consider non-constant holomorphic maps on Riemann surfaces and product of Riemann spheres, and we give conditions on the maps in order that they have arbitrary large prime numbers as periods. We use Lefschetz fixed point theory and in particular we compute the Lefschetz numbers of period m for large m's.

KEYWORDS:

• Lefschetz numbers
• holomorphic maps
• periodic point
• product of spheres
• torus

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 37C25
• 37C30
• 37E15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER), the Agència de Gestió d'Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.