3,832 research outputs found
Torus and Z/p actions on manifolds
Let G be either a finite cyclic group of prime order or S^1. We find new
relations between cohomology of a manifold (or a Poincare duality space) M with
a G-action on it and cohomology of the fixed point set, M^G. Our main tool is
the notion of Poincare duality on the Leray spectral sequence of the map M_G ->
BG. We apply our results to study group actions on 3-manifolds.Comment: To appear in Topology, 25 page
Skein theory for SU(n)-quantum invariants
For any n>1 we define an isotopy invariant, _n, for a certain set of
n-valent ribbon graphs Gamma in R^3, including all framed oriented links. We
show that our bracket coincides with the Kauffman bracket for n=2 and with the
Kuperberg's bracket for n=3. Furthermore, we prove that for any n, our bracket
of a link L is equal, up to normalization, to the SU_n-quantum invariant of L.
We show a number of properties of our bracket extending those of the Kauffman's
and Kuperberg's brackets, and we relate it to the bracket of
Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied
by _n, we define the SU_n-skein module of any 3-manifold M and we prove that
it determines the SL_n-character variety of pi_1(M).Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-36.ab
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