ar X iv : m at h / 04 01 05 6 v 1 [ m at h . G T ] 7 J an 2 00 4 SQUARE - TILED SURFACES IN H ( 2 )

ar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.

ar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

ar X iv : m at h / 05 01 04 7 v 1 [ m at h . FA ] 4 J an 2 00 5 On ( Co ) Homology of Triangular Banach

Suppose that A and B are unital Banach algebras with units 1A and 1B , respectively, M is a unital Banach A−B-bimodule, T =   A M 0 B   is the triangular Banach algebra, X is a unital T -bimodule, XAA = 1AX1A, XBB = 1BX1B , XAB = 1AX1B and XBA = 1BX1A. Applying two nice long exact sequences related to A, B, T , X, XAA, XBB , XAB and XBA we establish some results on (co)homology of triangu...

ar X iv : m at h / 05 04 55 2 v 1 [ m at h . N T ] 2 7 A pr 2 00 5 Multiple logarithms , algebraic cycles and trees

This is a short exposition—mostly by way of the toy models " double logarithm " and " triple logarithm " —which should serve as an introduction to the article [3] in which we establish a connection between multiple polylogarithms, rooted trees and algebraic cycles.

ar X iv : h ep - e x / 04 08 01 4 v 1 6 A ug 2 00 4 Plans for Kaon Physics at BNL