ar X iv : m at h / 06 07 11 6 v 1 [ m at h . G T ] 5 J ul 2 00 6 ON C n - MOVES FOR LINKS

ar X iv : m at h / 06 07 13 0 v 1 [ m at h . A G ] 5 J ul 2 00 6 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

ar X iv : m at h / 05 07 14 6 v 1 [ m at h . O A ] 7 J ul 2 00 5 EXACTNESS FROM PROPER ACTIONS

In this paper we show that if a discrete group G acts properly isometrically on a discrete space X for which the uniform Roe algebra C * u (X) is exact then G is an exact group. As a corollary, we note that if the action is cocompact then the following are equivalent: The space X has Yu's property A; C * u (X) is exact; C * u (X) is nuclear.

ar X iv : m at h / 06 11 07 6 v 4 [ m at h . G T ] 1 4 Fe b 20 09 Virtual Homotopy

Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, and self crossing changes. In this paper, we extend Milnor’s μ and μ̄ invariants to welded and virtual links. We conclude this paper with several examples, and compute the μ invariants using the Magnus expansion and Pol...

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