By Robert C. Penner

ISBN-10: 3037190752

ISBN-13: 9783037190753

There's an basically “tinker-toy” version of a trivial package deal over the classical Teichmüller house of a punctured floor, referred to as the embellished Teichmüller area, the place the fiber over some degree is the distance of all tuples of horocycles, one approximately every one puncture. This version ends up in an extension of the classical mapping category teams referred to as the Ptolemy groupoids and to convinced matrix versions fixing similar enumerative difficulties, every one of which has proved beneficial either in arithmetic and in theoretical physics. those areas take pleasure in a number of comparable parametrizations resulting in a wealthy and complicated algebro-geometric constitution tied to the already tricky combinatorial constitution of the tinker-toy version. certainly, the normal coordinates supply the prototypical examples not just of cluster algebras but in addition of tropicalization. This interaction of combinatorics and coordinates admits extra manifestations, for instance, in a Lie conception for homeomorphisms of the circle, within the geometry underlying the Gauss product, in profinite and pronilpotent geometry, within the combinatorics underlying conformal and topological quantum box theories, and within the geometry and combinatorics of macromolecules.

This quantity provides the tale and wider context of those adorned Teichmüller areas as constructed by way of the writer over the past twenty years in a chain of papers, a few of them in collaboration. occasionally correcting error or typos, occasionally simplifying proofs and occasionally articulating extra common formulations than the unique study papers, this quantity is self-contained and calls for little formal historical past. in response to a master’s direction at Aarhus collage, it provides the 1st therapy of those works in monographic shape.

Show description

Read Online or Download Decorated Teichmuller Theory PDF

Similar geometry books

Francois Baccelli, Bartlomiej Blaszczyszyn's Stochastic Geometry and Wireless Networks, Part II: PDF

Stochastic Geometry and instant Networks, half II: purposes makes a speciality of instant community modeling and function research. the purpose is to teach how stochastic geometry can be utilized in a kind of systematic approach to examine the phenomena that come up during this context. It first specializes in medium entry regulate mechanisms utilized in advert hoc networks and in mobile networks.

Get Variations, Geometry and Physics: In Honour of Demeter PDF

This ebook is a set of survey articles in a huge box of the geometrical thought of the calculus of diversifications and its purposes in research, geometry and physics. it's a commemorative quantity to have fun the sixty-fifth birthday of Professor Krupa, one of many founders of contemporary geometric variational conception, and an immense contributor to this subject and its purposes during the last thirty-five years.

Download e-book for iPad: Matrix Information Geometry by Jesús Angulo (auth.), Frank Nielsen, Rajendra Bhatia (eds.)

This e-book provides advances in matrix and tensor information processing within the area of sign, picture and data processing. The theoretical mathematical methods are discusses within the context of power functions in sensor and cognitive structures engineering. the subjects and alertness contain info Geometry, Differential Geometry of based Matrix, optimistic sure Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and functions in Cognitive structures, particularly facts Mining.

Additional info for Decorated Teichmuller Theory

Sample text

Proof. 13.

4 and the definition of continued fractions) is left to the reader. 4, we may identify these two sets. Z/, then we let A act on the right on the points at infinity (following Gauss’ convention in fact), and hence on oriented geodesics, and shall thus identify an oriented edge of with the image under the right action of A of the distinguished oriented edge from 0 to 1. 3. Furthermore, reversing the orientation on an edge labeled A corresponds to re-labeling SA. Another number-theoretic aspect of the current discussion involves so-called elliptic curves, namely, discrete subgroups ƒ of C of rank 2, also called lattices.

Minkowski three-space. x; y; z/ 2 R3 W hu; ui D C1g: Notice that if u; v 2 LC , then hu; vi Ä 0 with equality if and only if u is a scalar multiple of v, and if u 2 LC ; v 2 H, then hu; vi < 0, where both inequalities follow from the Cauchy–Schwarz inequality. LC [ LC / has the corresponding attribute. One checks without difficulty that a plane … D fu 2 R3 W hu; vi D g with Minkowski normal v, for some 2 R, is elliptic, parabolic, or hyperbolic, respectively, if and only if hv; vi is negative, vanishes, or is positive.

Download PDF sample

Decorated Teichmuller Theory by Robert C. Penner

by Ronald

New PDF release: Decorated Teichmuller Theory
Rated 4.17 of 5 – based on 17 votes
[an error occurred while processing the directive]