Fixed points on trivial surface bundles over a connected CW-complex

Abstract

The main purpose of this work is to study fixed points of fibre-preserving maps over a connected CW-complex B on the trivial surface bundles B×S where S is a closed surface of negative Euler characteristic. The case where B = S1 and S is equal to S2, i.e., the closed orientable surface of genus 2, is already known. We classify all such maps that can be deformed fibrewise to a fixed point free map.