ar X iv : m at h / 06 07 35 6 v 1 [ m at h . D G ] 1 4 Ju l 2 00 6 COMPLETE MANIFOLDS WITH NONNEGATIVE

ar X iv : m at h / 06 07 26 1 v 2 [ m at h . D G ] 1 2 Ju l 2 00 6 Fourier expansion along geodesics

A growth estimate on the Fourier coefficients along geodesics for eigenfunctions of the Laplacian is given on compact hyperbolic manifolds. Along the way, a new summation formula is proved.

ar X iv : m at h / 06 07 79 4 v 1 [ m at h . G T ] 3 1 Ju l 2 00 6 MUTATION AND THE COLORED JONES POLYNOMIAL

We show examples of knots with the same polynomial invariants and hyperbolic volume, with variously coinciding 2-cable polynomials and colored Jones polynomials, which are not mutants. AMS Classifications: 57M25, 57N70

ar X iv : m at h / 06 07 37 6 v 1 [ m at h . G T ] 1 6 Ju l 2 00 6 Asymptotic dimension and uniform embeddings

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any l) compression. The method allows to obtain the lower bound of the compression of the lamplighter group Z≀Z, which has infinite asymptotic dimension.

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 04 07 44 1 v 1 [ m at h . SG ] 2 6 Ju l 2 00 4 THE GEOMETRY OF SYMPLECTIC PAIRS

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.