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245 00 Geometry, topology and dynamics of character varieties /
|ceditors, William Goldman, Caroline Series, Ser Peow Tan.
264 1 Hackensack, N.J. :|bWorld Scientific,|c2012.
300 1 online resource (xi, 349 pages :) :|billustrations.
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
340 |gpolychrome|2rdacc
347 text file|2rdaft
490 1 Lecture notes series. Institute for Mathematical Sciences,
National University of Singapore ;|vv. 23
504 Includes bibliographical references.
505 0 Foreword; Preface; An Invitation to Elementary Hyperbolic
Geometry Ying Zhang; Introduction; 1. Euclid's Elements,
Book I and Neutral Plane Geometry; 1.1. A brief review of
contents of Elements, Book I; 1.2. A useful lemma; 1.3. A
gure-free proof of Proposition I.7; 1.4. More notes on
Elements, Book I; 1.5. Playfair's axiom; 1.6. Neutral
plane geometry; 1.7. Angle-sums of triangles and
Legendre's Theorems; 1.8. Quadrilaterals with two
consecutive right angles; 1.9. Saccheri and Lambert
quadrilaterals; 1.10. Variation of triangles in a neutral
plane.
505 8 1.11. A midline configuration for triangles1.12. More
theorems of neutral plane geometry; 1.13. Small angles; 2.
Hyperbolic Plane Geometry; 2.1. Hyperbolic plane; 2.2.
Asymptotic Parallelism; 2.3. Angle of parallelism; 2.4.
The variation in the distance between two straight lines;
2.5. Some more theorems in hyperbolic plane geometry; 2.6.
Construction of the common perpendicular to two ultra-
parallel straight lines; 2.7. Construction of asymptotic
parallels; 2.8. Ideal points; 2.9. Horocycles; 2.10.
Construction of the straight line joining two given ideal
points; 2.11. Ultra-ideal points.
505 8 2.12. The projective plane associated to a hyperbolic
plane2.13. Center-pencils of a hyperbolic triangle; 2.14.
Equidistant curves; 2.15. Positions of proper points
relative to an ideal point; 2.16. Hyperbolic areas via
equivalence of triangles; 2.17. Metric relations of
corresponding arcs in concentric horocycles; 3. Isometries
of the Hyperbolic Plane; 3.1. Isometries and reections in
straight lines; 3.2. Orientation preserving/reversing
isometries; 3.3. Rotations; 3.4. Translations; 3.5.
Isometries of parabolic type; 3.6. Redundancy of two
reflections.
505 8 3.7. Orientation reversing isometries as reflections and
glide reflections3.8. Isometries as projective
transformations; 3.9. Invariant projective lines of; 3.10.
Composition of two orientation preserving isometries other
than two translations; 3.11. Composition of two
translations; 3.12. Conjugates of isometries; 3.13. The
orthic triangle; 4. Hyperbolic Trigonometry Derived from
Isometries; 4.1. Some identities of isometries of a
neutral plane; 4.2. Some trigonometric formulas in H2(k);
4.3. Upper half-plane model U2 for hyperbolic plane H2(1);
4.4. Matrices of certain isometries of U2.
505 8 4.5. Trigonometric laws via identities of isometries4.6.
Suggested further readings; Acknowledgments; References;
Hyperbolic Structures on Surfaces Javier Aramayona; 1.
Introduction; 2. Plane Hyperbolic Geometry; 2.1. Mobius
transformations; 2.1.1. Classification in terms of trace
and fixed points; 2.2. Models for hyperbolic geometry;
2.2.1. Hyperbolic distance; 2.2.2. Mobius transformations
act by isometries; 2.2.3. The Cayley transformation;
2.2.4. Hyperbolic geodesics; 2.2.5. The boundary at
infinity; 2.2.6. The full isometry group; 2.2.7. Dynamics
of elements of Isom+(H).
520 This volume is based on lectures given at the highly
successful three-week Summer School on Geometry, Topology
and Dynamics of Character Varieties held at the National
University of Singapore's Institute for Mathematical
Sciences in July 2010. Aimed at graduate students in the
early stages of research, the edited and refereed articles
comprise an excellent introduction to the subject of the
program, much of which is otherwise available only in
specialized texts. Topics include hyperbolic structures on
surfaces and their degenerations, applications of ping-
pong lemmas in various contexts, intro.
590 eBooks on EBSCOhost|bEBSCO eBook Subscription Academic
Collection - North America
650 0 Topology.|0https://id.loc.gov/authorities/subjects/
sh85136089
650 7 Topology.|2fast|0https://id.worldcat.org/fast/1152692
655 0 Electronic books.
655 4 Electronic books.
700 1 Goldman, William.
700 1 Series, Caroline.|0https://id.loc.gov/authorities/names/
n90697973
700 1 Tan, Ser Peow.|0https://id.loc.gov/authorities/names/
no2012130488
776 08 |iPrint version:|aGoldman, William.|tGeometry, Topology
and Dynamics of Character Varieties.|dSingapore : World
Scientific, ©2012|z9789814401357
830 0 Lecture notes series (National University of Singapore.
Institute for Mathematical Sciences) ;|0https://id.loc.gov
/authorities/names/no2003042729|vv. 23.
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
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db=nlebk&AN=479888|zOnline eBook. Access restricted to
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856 42 |3Instructions for reading/downloading this eBook|uhttp://
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