ar X iv : 0 90 7 . 07 87 v 1 [ m at h . G R ] 4 J ul 2 00 9 Submonoids and rational subsets of groups with infinitely many ends

ar X iv : 1 30 2 . 24 55 v 1 [ m at h . G R ] 1 1 Fe b 20 13 Rational subsets and submonoids of wreath products ⋆

It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z ≀ Z with an undecidable membership problem.

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 : 0 90 5 . 02 56 v 1 [ m at h . G R ] 3 M ay 2 00 9 REMARKS ON PROFICIENT GROUPS

If a finite group G has a presentation with d generators and r relations, it is well-known that r−d is at least the rank of the Schur multiplier of G; a presentation is called efficient if equality holds. There is an analogous definition for proficient profinite presentations. We show that many perfect groups have proficient presentations. Moreover, we prove that infinitely many alternating gro...

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 80 7 . 00 58 v 1 [ m at h . D G ] 1 J ul 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.