Higher Bers maps

Higher Order Phantom Maps

For each ordinal number α, we define phantom maps of order α. We construct universal phantom maps out ofX with order α, and show that under easily verifiable conditions, every one of these universal phantom maps is essential. Math. Subject Classifications: 55P05, 55S36

Mathema Tics: L. Bers

Maps between Higher Bruhat Orders and Higher Stasheff-tamari Posets

We make explicit a description in terms of convex geometry of the higher Bruhat orders B(n, d) sketched by Kapranov and Voevodsky. We give an analogous description of the higher Stasheff-Tamari poset S1(n, d). We show that the map f sketched by Kapranov and Voevodsky from B(n, d) to S1([0, n + 1], d + 1) coincides with the map constructed by Rambau, and is a surjection for d ≤ 2. We also give g...

On Approximation in the Bers Spaces

Let D be a Jordan domain in the complex plane with rectifiable boundary C. Let Aq(D) denote the Bers space with norm || ||,. We prove that if/6 A„(D), 2<q<cc, then there exist functions ■s„W = 2£=i l/(z — zn!c), znltEC for k = \,■ ■ ,n, such that \Un— f\\«—"-0This result does not hold for 1 <q^2 even when D is a disc.

On the Bers Fiber Spaces

It is well known that a Bers fiber space F (Γ) for a torsion free finitely generated Fuchsian group Γ of the first kind can be identified with a Teichmüller space. If Γ has torsion, a theorem of Earle–Kra [9] asserts that in almost all cases, F (Γ) is not isomorphic to any Teichmüller space. However, there are 39 cases which remain unsettled. Our results remove 27 from the 39 previously unknown...