Rice University Math Department Calendar

    February 2011            March 2011             April 2011     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5          1  2  3  4  5                   1  2
  6  7  8  9 10 11 12    6  7  8  9 10 11 12    3  4  5  6  7  8  9
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 27 28                  27 28 29 30 31         24 25 26 27 28 29 30

11:00 am Tuesday, March 15, 2011
Oral Defense: Self-Inverses in Rauzy Classes
by Jon Fickenscher (Rice University) in HB 227

Thanks to works by M. Kontsevich and A. Zorich followed by C. Boissy, we have a classification of all Rauzy Classes of any given genus. It follows from these works that Rauzy Classes are closed under the operation of inverting the permutation. In this paper, we shall prove the existence of self-inverse permutations in every Rauzy Class by giving an explicit construction of such an element satisfying the sufficient conditions. As a corollary, we will give another proof that every Rauzy Class is closed under taking inverses. In the case of generalized permutations, generalized Rauzy Classes have been classified by works of M. Kontsevich, H. Masur and J. Smillie, E. Lanneau, and again C. Boissy. We state the definition of self-inverse for generalized permutations and prove a necessary and sufficient condition for a generalized Rauzy Class to contain self-inverse elements.Host Department: Rice University-Mathematics
Submitted by jonfick@rice.edu