Browsing by Subject "moduli space"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    COMPUTING DYNAMICAL DEGREES OF RATIONAL MAPS ON MODULI SPACE
    (Cambridge, 2015) Koch, Sarah; Roeder, Roland K.; Department of Mathematical Sciences, School of Science
    The dynamical degrees of a rational map f:X⇢X are fundamental invariants describing the rate of growth of the action of iterates of f on the cohomology of X. When f has non-empty indeterminacy set, these quantities can be very difficult to determine. We study rational maps f:XN⇢XN, where XN is isomorphic to the Deligne–Mumford compactification M¯¯¯¯0,N+3. We exploit the stratified structure of XN to provide new examples of rational maps, in arbitrary dimension, for which the action on cohomology behaves functorially under iteration. From this, all dynamical degrees can be readily computed (given enough book-keeping and computing time). In this paper, we explicitly compute all of the dynamical degrees for all such maps f:XN⇢XN, where dim(XN)≤3 and the first dynamical degrees for the mappings where dim(XN)≤5. These examples naturally arise in the setting of Thurston’s topological characterization of rational maps.
  • Thumbnail Image
    Item
    Fundamental groups of character varieties: surfaces and tori
    (Springer, 2015-10) Biswas, Indranil; Lawton, Sean; Ramras, Daniel; Department of Mathematical Sciences, School of Science
    We compute the fundamental group of moduli spaces of Lie group valued representations of surface and torus groups.