Fixed simplex property for retractable complexes (Q610891)

The following are the main results of the paper: I) A star has the fixed point property; II) If an \(\leq n\)-complex is retractable, then it has the fixed point property; III) From an \(s\)-recursively retractable complex \(K_{\leq n}\), by a sequence of retractions, one can obtain the complex generated by any simplex \(S\in K_{\leq n}\). Some applications to graph theory of the obtained results are then given.