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

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 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 : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 03 09 40 8 v 2 [ m at h . D G ] 1 2 Ju l 2 00 4 EINSTEIN METRICS ON SPHERES

ar X iv : m at h / 06 07 71 6 v 1 [ m at h . D G ] 2 7 Ju l 2 00 6 THE SPINORIAL τ - INVARIANT AND 0 - DIMENSIONAL SURGERY

Let M be a compact manifold with a metric g and with a fixed spin structure χ. Let λ + 1 (g) be the first non-negative eigenvalue of the Dirac operator on (M, g, χ). We set τ (M, χ) := sup inf λ + 1 (g) where the infimum runs over all metrics g of volume 1 in a conformal class [g 0 ] on M and where the supremum runs over all conformal classes [g 0 ] on M. Let (M # , χ #) be obtained from (M, χ)...