# Download Discrete Groups and Geometric Structures: Workshop on by Karel Dekimpe, Paul Igodt, Alain Valette PDF

By Karel Dekimpe, Paul Igodt, Alain Valette

This quantity experiences on examine with regards to Discrete teams and Geometric buildings, as offered throughout the foreign Workshop held could 26-30, 2008, in Kortrijk, Belgium. Readers will take advantage of amazing survey papers by means of John R. Parker on how you can build and examine lattices in complicated hyperbolic house and through Ursula Hamenstadt on homes of team activities with a rank-one point on right CAT (0)-spaces. This quantity additionally includes study papers within the region of staff activities and geometric constructions, together with paintings on loops on a two times punctured torus, the simplicial quantity of goods and fiber bundles, the homology of Hantzsche - Wendt teams, tension of actual Bott towers, circles in teams of tender circle homeomorphisms, and teams generated via backbone reflections admitting crooked basic domain names

**Read or Download Discrete Groups and Geometric Structures: Workshop on Discrete Groups and Geometric Structures, With Applications Iii: May 26-30, 2008: Kortrijk, Belgium PDF**

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**Additional resources for Discrete Groups and Geometric Structures: Workshop on Discrete Groups and Geometric Structures, With Applications Iii: May 26-30, 2008: Kortrijk, Belgium**

**Example text**

Parker; The geometry of Picard modular groups. Preprint. [17] E. R. Parker; The geometry of the Eisenstein-Picard modular group. Duke Math. J 131 (2006), 249–289. [18] G. D. Lax; An explicit fundamental domain for the Picard modular group in two complex dimensions. Proc. Nat. Acad. Sci. USA 103 (2006), 11103–11105. ´ [19] G. Giraud, Sur certaines fonctions automorphes de deux variables. Ann. Sci. Ecole Norm. Sup. 38 (1921), 43–164. M. Goldman; Complex Hyperbolic Geometry. Oxford University Press, 1999.

Monodromy groups and equilateral triangle groups. Consider the map R1 , which is the holonomy around L23 . This is a complex reﬂection ﬁxing L23 with angle 2π/p. Similarly, R2 and A1 are the holonomies around L13 and L14 . These are complex reﬂections with angles 2π/p and 2π/k. Thinking of the cone points v1 , . . , v5 as marked points on the sphere, we can think of R1 , R2 , A1 as elements of the mapping class group of the ﬁve punctured sphere. There is a well known relation between the mapping class group and the braid group; see Birman’s book [7].

Hence these groups are Mostow groups of the ﬁrst type. 1. • In the second block 1/l > 0 and 1/d ≤ 0. This means that Aj is a complex reﬂection in a complex line and P 3 is a complex reﬂection in a point or is parabolic. 3. • In the third block 1/l < 0 and 1/d > 0. Thus Aj is a complex reﬂection in a point and P 3 is a complex reﬂection in a line. 2 • In the fourth block 1/l and 1/d are both positive. Indeed, k = 3 and l = 3d. In this case, Aj and P 3 are both complex reﬂections in complex lines.