Celebratio Mathematica — Birman

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Works connected to José María Montesinos Amilibia

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J. S. Birman, F. González-Acuña, and J. M. Montesinos: “Heegaard splittings of prime 3-manifolds are not unique,” Michigan Math. J. 23 : 2 (1976), pp. 97–103. MR 0431175 Zbl 0321.57004 article

José María Montesinos Amilibia	Related
Francisco Javier González-Acuña	Related

J. S. Birman and J. M. Montesinos: “On minimal Heegaard splittings,” Michigan Math. J. 27 : 1 (1980), pp. 47–56. MR 555836 Zbl 0436.57003 article

In 1936 J. H. C. Whitehead developed an algorithm for transforming a set of words in a free group to a new set which has minimum length among all systems which are equivalent to the given system under automorphisms of the free group (see [Whitehead 1936] and also [Higgins and Lyndon 1974]). Whitehead’s stated motivation for studying this question was related (but different) topological question: if a Heegard diagram for a 3-manifold \( M \) does not have minimal genus, is there an algorithm for systematically reducing the genus and then further modifying the diagram to some “simplest” possible diagram for that \( M \)? (See section 4 of [Whitehead 1936].) Such an algorithm would in certain cases solve the homeomorphism problem for 3-manifolds. The results of Whitehead were later sharpened by Zieschang [1970], with further positive contributions by Waldhausen [1968, 1978].