Handel’s Fixed Point Theorem: A Morse Theoretical Point of View

Michael Handel has proved in [10] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that turned out to be efficient tool study dynamics surface homeomorphisms. The present article fits into series articles by author [13] and Juliana Xavier [21, 22], where proofs were given, related classical Brouwer Theory, instead Homotopical Theory used original article. Like [13, 21] [22], we will use “free brick decompositions” but more conceptual Morse theoretical argument. It is based on new preliminary lemma, gives nice “condition at infinity” our problem.