A note on a multi-variable polynomial link invariant
Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth (A remark on the paper of M. Cowling et al.)
We study spectral multipliers for a distinguished Laplacian on certain groups of exponential growth. We obtain a stronger optimal version of the results proved in [CGHM] and [A].
Skein algebra of a group
We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show...
A smooth subadditive homogeneous norm on a homogeneous group
Riesz meets Sobolev
We show that the boundedness, p > 2, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.
L₁-uniqueness of degenerate elliptic operators
Let Ω be an open subset of with 0 ∈ Ω. Furthermore, let be a second-order partial differential operator with domain where the coefficients are real, and the coefficient matrix satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If for some λ > 0 where then we establish that is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup. Moreover...
Skein theory for -quantum invariants.
Heat kernels and Riesz transforms on nilpotent Lie groups
We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds...
Categorification of the Kauffman bracket skein module of -bundles over surfaces.
Page 1