Periods for holomorphic maps via Lefschetz numbers

Jaume Llibre,Michael Todd

doi:10.1155/aaa.2005.575

Jaume Llibre, Michael Todd

Open Access

https://doi.org/10.1155/aaa.2005.575

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Abstract

We characterise the set of fixed points of a class of holomorphic maps on complex manifolds with a prescribed homology. Our main tool is the Lefschetz number and the action of maps on the first homology group.

Highlights

Introduction and main result In this note we are concerned with fixed point theory for holomorphic self maps on complex manifolds
We prove a similar theorem for periodic points of holomorphic maps of complex manifolds with a prescribed homology
We use a result of Fagella and Llibre in [3] which relates the Lefschetz number to the set of fixed points for holomorphic maps on compact complex manifolds

Summary

Introduction

1. Introduction and main result In this note we are concerned with fixed point theory for holomorphic self maps on complex manifolds. After the well-known Schwarz lemma on the unit disk, which assumes a fixed point, the Pick theorem was proved in [8]. We prove a similar theorem for periodic points of holomorphic maps of complex manifolds with a prescribed homology.

Results

Conclusion