By Allan J. Sieradski

The therapy of the topic of this article isn't encyclopedic, nor was once it designed to be appropriate as a reference guide for specialists. quite, it introduces the subjects slowly of their ancient demeanour, in order that scholars aren't beaten by way of the last word achievements of a number of generations of mathematicians. cautious readers will see how topologists have steadily subtle and prolonged the paintings in their predecessors and the way such a lot solid principles succeed in past what their originators predicted. To motivate the improvement of topological instinct, the textual content is abundantly illustrated. Examples, too quite a few to be thoroughly coated in semesters of lectures, make this article appropriate for self sustaining learn and make allowance teachers the liberty to pick what they are going to emphasize. the 1st 8 chapters are compatible for a one-semester path normally topology. the whole textual content is appropriate for a year-long undergraduate or graduate point curse, and gives a robust starting place for a next algebraic topology path dedicated to the better homotopy teams, homology, and cohomology.

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142(1979), 221–274. [81] D. Johnson and J. , 1984), Progr. Math. 67, Birkhäuser, 1987, 48–106. [82] T. Jørgensen and A. Marden, “Algebraic and geometric convergence of Kleinian groups,” Math. Scand. 66(1990), 47–72. [83] M. Kapovich, Hyperbolic Manifolds and Discrete groups: Lectures on Thurston’s Hyperbolization, Birkhauser, 2000. [84] S. Katok, Fuchsian groups, University of Chicago Press, 1992. [85] L. Keen and C. Series, “Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori,” Topology 32(1993), 719–749.

33] B. Bowditch, “Geometrical finiteness for hyperbolic groups,” J. Funct. Anal. 113(1993), 245–317. [34] M. Bridgeman, “Average bending of convex pleated planes in hyperbolic threespace,” Invent. Math. 132(1998), 381–391. [35] M. Bridgeman, “Bounds on the average bending of the convex hull of a Kleinian group,” Mich. Math J. 51(2003), 363–378. [36] M. D. Canary, “From the boundary of the convex core to the conformal boundary,” Geom. Ded. 96(2003), 211–240. [37] M. D. Canary, “Bounding the bending of a hyperbolic 3-manifold,” Pac.

D. P. Kerckhoff, “Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery,” J. Diff. Geom. 48(1998), 1–59. [78] J. Holt, “Some new behaviour in the deformation theory of Kleinian groups,” Comm. Anal. Geom 9(2001), 757–775. [79] J. Holt, “Multiple bumping of components of deformation spaces of hyperbolic 3-manifolds,” Amer. J. , 125(2003), 691–736. [80] J. Hubbard and H. Masur, “Quadratic differentials and foliations,” Acta Math. 142(1979), 221–274. [81] D. Johnson and J. , 1984), Progr.

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