ar X iv : m at h / 06 06 43 5 v 1 [ m at h . G T ] 1 9 Ju n 20 06 PROPERTIES OF CLOSED 3 - BRAIDS

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : m at h / 06 06 43 6 v 1 [ m at h . Q A ] 1 9 Ju n 20 06 NONCOMMUTATIVE POISSON STRUCTURES ON ORBIFOLDS

In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of C∞(M)⋊Γ. Using this computation, we classify all the noncommutative Poisson structures on C∞(M) ⋊ Γ when M is a symplectic manifold. We provide examples of deformation quantizations of these noncommutative Poisson structures.

ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE

ar X iv : m at h / 06 06 27 5 v 1 [ m at h . A T ] 1 2 Ju n 20 06 MODULES IN MONOIDAL MODEL CATEGORIES

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

ar X iv : m at h / 05 06 37 9 v 1 [ m at h . G N ] 1 9 Ju n 20 05 Residuality of Families of F σ Sets Shingo

We prove that two natural definitions of residuality of families of Fσ sets are equivalent. We make use of the Banach-Mazur game in the proof.