ar X iv : 0 70 8 . 19 90 v 1 [ m at h . A G ] 1 5 A ug 2 00 7 RATIONAL SINGULARITIES ASSOCIATED TO PAIRS

ar X iv : 0 70 8 . 05 14 v 1 [ m at h . G T ] 3 A ug 2 00 7 Invariants of genus 2 mutants

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 2-variable polynomials, answering a question raised by Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v =...

ar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO

ar X iv : 0 90 8 . 27 37 v 1 [ m at h . G R ] 1 9 A ug 2 00 9 On Bruck Loops of 2 - power Exponent , II ∗

As anounced in [BSS], we show that the non-passive finite simple groups are among the PSL2(q) with q − 1 ≥ 4 a 2-power.

ar X iv : 0 70 8 . 22 12 v 1 [ m at h . C O ] 1 6 A ug 2 00 7 Enumerative properties of NC ( B ) ( p , q )

We determine the rank generating function, the zeta polynomial and the Möbius function for the poset NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers.

ar X iv : 0 90 8 . 19 89 v 1 [ m at h . A G ] 1 3 A ug 2 00 9 D - MODULES ON 1 | 1 SUPERCURVES

It is known that to every (1|1) dimensional supercurve X there is associated a dual supercurve X̂ , and a superdiagonal ∆ ⊂ X × X̂. We establish that the categories of D-modules on X , X̂ and ∆ are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with co...