Some examples concerning homotopies of fixed point free maps (Q752537)

The author gives an example of two homotopic p.l. maps \(f_ 0,f_ 1: M\to M\) which are fixed point free but any homotopy between the two maps must have a nonempty fixed point set. The manifold M is compact and \(\partial M\neq \emptyset\). In order to prove his result he uses a lemma which provides a special homotopy G between \(f_ 0\) and \(f_ 1\).