1,243 research outputs found
Twisted Alexander polynomials and incompressible surfaces given by ideal points
We study incompressible surfaces constructed by Culler-Shalen theory in the
context of twisted Alexander polynomials. For a st cohomology class of a
-manifold the coefficients of twisted Alexander polynomials induce regular
functions on the -character variety. We prove that if an
ideal point gives a Thurston norm minimizing non-separating surface dual to the
cohomology class, then the regular function of the highest degree has a finite
value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary",
the Journal of Mathematical Sciences, the University of Toky
Reflection Groups and Polytopes over Finite Fields, III
When the standard representation of a crystallographic Coxeter group is
reduced modulo an odd prime p, one obtains a finite group G^p acting on some
orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p
will often be the automorphism group of a finite abstract regular polytope. In
parts I and II we established the basics of this construction and enumerated
the polytopes associated to groups of rank at most 4, as well as all groups of
spherical or Euclidean type. Here we extend the range of our earlier criteria
for the polytopality of G^p . Building on this we investigate the class of
3-infinity groups of general rank, and then complete a survey of those locally
toroidal polytopes which can be described by our construction.Comment: Advances in Applied Mathematics (to appear); 19 page
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