The following papers are in inverse coronological order.

  • On the complexity of the word problem in the mapping class groups and braid groups (July 28,1997)(Postscript format, 630K)

    Here I prove that the complexity of the word problem in the mapping class group of a closed surface of genus g is O(|w|2g2) for |w|>log g ,where |w| is the word length. I prove a corresponding bound for the mapping class group of the punctured surfaces. Same methods yield a new bound for the word problem in the braid groups; namely O(|w|2n) for |w|>log n, where n is the braid index.
  • On free subgroups of the mapping class group (May 15, 1997) (Postscript format; 640K)

    Here I give bounds for integers m,n sufficient to make <fm,gn> a free group, for a pair of pseudo Anosov mapping classes f,g.
  • My Ph.D. Thesis: Algorithms in the surface mapping class groups (April 23, 1997) (Postscript format; 1.2M)

    • This thesis was done in Columbia University under the advisement of Joan Birman.

  • A translation of the following paper to English: Bridge representations of the trivial knot by Jean-Pierre Otal (Feb 1997) (Postscript format; 290K)

    • This paper is originally in French. It contains a proof of the following: Any two bridge perpresentations of the trivial knot are equivalent.

  • A translation of the following paper to English: On the minimum dilitation of a pseudo-Anosov diffeomorphism of a two holed torus by A. Yu. Zhirov (Jan 1997)(Postscript format; 253K)

    • This paper is originally in Russian. It contains a proof of the following: For a pseudo-Anosov diffeomorphism of a surface of genus 2 with orientable fixed foliations, the dilitation is bigger than or equal to 1.722083...

  • Surface diffeomorphisms via train-tracks     with    Zong-He Chen
    Topology and its Applications 73 (1996) 141-167

    This paper gives a treatment of the pi1-train-track normal forms for measured train-tracks. One can use this to find the image of a measured train-track under a mapping class; This gives another algorithm to decide on Nielsen-Thurston tricothomy: Pseudo-Anosov, reducible, or finite order.