By Mario Bonk, Jane Gilman, Howard Masur, yair Minsky, Michael Wolf
The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The center of this legacy lies within the fields of geometric functionality conception, Teichmuller idea, hyperbolic geometry, and partial differential equations. in spite of the fact that, the paintings of Ahlfors and Bers has impacted and created interactions with many different fields of arithmetic, equivalent to algebraic geometry, dynamical platforms, topology, geometric workforce thought, mathematical physics, and quantity idea. fresh years have noticeable a flowering of this legacy with an elevated curiosity of their paintings. This present quantity comprises articles on a wide selection of matters which are crucial to this legacy. those comprise papers in Kleinian teams, classical Riemann floor conception, translation surfaces, algebraic geometry and dynamics. the vast majority of the papers current new study, yet there are survey articles to boot
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97(1989), 553–583. [Ve2] William A. Veech. Delaunay partitions. Topology 36(1997), 1–28. [Ve3] William A. Veech. Bicuspid F -structures and Hecke groups. Preprint. [Zo] Anton Zorich. Square tiled surfaces and Teichm¨ uller volumes of the moduli spaces of abelian differentials. In Rigidity in dynamics and geometry (Cambridge, 2000), pages 459–471. Springer, Berlin, 2002. Department of Mathematics, Cornell University, Ithaca, NY 14853 This page intentionally left blank Contemporary Mathematics Volume 510, 2010 A family of Riemann surfaces with orientation reversing automorphisms Emilio Bujalance and Francisco-Javier Cirre Abstract.
2] for a general account on this topic. The orientation reversing isometries of D are either reflections (of order two) or glide reflections (of infinite order). Here we shall deal with proper NEC groups (that is, groups which contain orientation reversing elements) with no reflection. If Λ is such a group then it has a presentation by means of generators and defining relations of the form mr 1 d1 , . . , dγ , x1 , . . , xr | xm = x1 · · · xr d21 · · · d2γ = 1 , 1 = · · · = xr where d1 , . . , dγ are glide reflections and x1 , .
Xp } and {y1 , . . , yp } a generator µX (γ) acts on the set of points Pij = xi + yj by xi + yj → xg(j) + yh(i) , and since it is an involution h = g −1 , so that every generator µX (γ) is an element of the set Xn defined in §5. The subgroup Γ0 corresponding to the covering X is the estabilizer of a point Pij = xi + yj . 1, whence G must equal Σ. 40 6 LUIS ARENAS-CARMONA AND ANITA M. ROJAS 4. Unramified p−covers of hyperelliptic curves and pairs of p−gonal covers. We came to the main geometric result of the work, which generalizes [LRR] Thm.