A minimum fixed point theorem for smooth fiber preserving maps

Abstract

Let p : E → B p:E\rightarrow B be a smooth fiber bundle. Given a smooth fiber preserving map f : E → E f:E\rightarrow E , we will show that f f can be deformed by a smooth, fiber preserving homotopy to a smooth map g : E → E g:E\rightarrow E such that the number of fixed points of g g is equal to the fiberwise Nielsen number of f f .