16.     15. A fake Schottky group in Mod(S) (with C. J. Leininger) (submitted)   New. We use the classical construction of Schottky groups in hyperbolic geometry to produce non-Schottky subgroups of the mapping class group.     14. Bers slices are Zariski dense (with D. Dumas) (submitted)   New. We prove that a Bers slice is always Zariski dense in the SL(2,C)–character variety of the surface.     13. Intersections and joins of free groups to appear in Algebraic & Geometric Topology Let H and K be subgroups of a free group of ranks h and k ≥ h. We prove the following strong form of Burns' inequality:         rank(H∩K) – 1   ≤   2(h–1)(k–1) – (h–1)(rank(HVK) –1). A corollary of this, also obtained by L. Louder and D. B. McReynolds, has been used by M. Culler and P. Shalen to obtain information regarding the volumes of hyperbolic 3–manifolds. We also prove the following particular case of the Hanna Neumann Conjecture, which has also been obtained by Louder. If HVK has rank at least (h + k + 1)/2, then H∩K has rank no more than (h–1)(k–1) + 1.     12. Slicing, skinning, and grafting (with D. Dumas) to appear in the American Journal of Mathematics We prove that a Bers slice is never algebraic. A corollary is that skinning maps are never constant.     11. trees and mapping class groups (with C. J. Leininger and S. Schleimer) (submitted) There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the kernel of this map are convex cocompact in the sense of B. Farb and L. Mosher. In particular, we obtain an affirmative answer to their question of local convex cocompactness of K. Whittlesey's group. In the course of the proof, we obtain a new proof of a theorem of Kra. We also relate the action of this kernel on the curve complex to a family of actions on trees. This quickly yields a new proof of a theorem of J. Harer.     10. skinning maps (submitted)   Clarifying Revision 3.5.08. Let M be a hyperbolic 3–manifold with nonempty totally geodesic boundary. We prove that there are upper and lower bounds on the diameter of the skinning map of M that depend only on the volume of the hyperbolic structure with totally geodesic boundary, answering a question of Y. Minsky. This is proven via a filling theorem, which states that as one performs higher and higher Dehn fillings, the skinning maps converge uniformly on all of Teichmüller space. We also exhibit manifolds with totally geodesic boundaries whose skinning maps have diameter tending to infinity, as well as manifolds whose skinning maps have diameter tending to zero (the latter are due to K. Bromberg and the author). In the final section, we give a proof of Thurston's Bounded Image Theorem.     9. Subgroups of mapping class groups from the geometrical viewpoint (with C. J. Leininger)* In the tradition of Ahlfors–Bers, IV, 119–141. Contemp. Math., 432, Amer. Math. Soc., Providence, RI, 2007. We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.     8. Uniform convergence in the mapping class group (with C. J. Leininger)* Ergodic Theory and Dynamical Systems (2008), 28, 1177–1195. We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact. published version from Cambridge University Press     7. Shadows of mapping class groups: capturing convex cocompactness (with C. J. Leininger)* to appear in Geometric and Functional Analysis. We strengthen the analogy between convex cocompact Kleinian groups and convex cocompact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).     6. Surface groups are frequently faithful (with J. DeBlois) Duke Mathematical Journal 131, no. 2 (2006), 351–362. If S is a closed hyperbolic surface, the set of faithful representations is dense in the PSL(2,K) representation variety of the fundamental group of S, where K is the field of real or complex numbers. This answers a question of W. Goldman. We also prove the existence of faithful representations into PU(2,1) with certain nonintegral Toledo invariants. published version at Project Euclid     5. Totally geodesic boundaries of knot complements Proceedings of the American Mathematical Society 133 (2005), 3735–3744. Given a compact orientable 3–manifold M whose boundary is a hyperbolic surface and a simple closed curve C in its boundary, every knot in M is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of C is as small as you like. published version at the American Mathematical Society     4. Achievable ranks of intersections of finitely generated free groups International Journal of Algebra and Computation, Vol. 15 No. 2 (2005) 339–341. Given a free group F and integers m and n greater than zero, all numbers between 0 and (m–1)(n–1) + 1 occur as the rank of the intersection of two subgroups H and K of ranks m and n. published version available through WorldSciNet     3. A short proof that composite twisted unknots are singly twisted unknots Journal of Knot Theory and its Ramifications 13 (2004), no. 7, 873–875. A short proof is given of a theorem of Hayashi and Motegi and (independently) Goodman–Strauss that only singly twisted unknots are composite. published version available through WorldSciNet     2. Bundles, handcuffs, and local freedom Geometriae Dedicata 106 (2004), 145–159. A commensurably infinite collection of fibered hyperbolic 3–manifolds whose groups contain subgroups that are locally free and not free is constructed. published version available through Springer     1. A geometric and algebraic description of annular braid groups [no figures] (with D. Peifer) International Journal of Algebra and Computation, Vol. 12, Nos. 1 & 2 (2002) 85–97. We show that Artin's Braid group is virtually a semidirect product of the affine braid group and the group of integers. published version available through WorldSciNet       Lecture notes to Cameron Gordon's course on Normal Surface Theory [from Spring 2001] (including a proof of the Disk Theorem (a.k.a. Loop Theorem–Dehn's Lemma) with no tower!) available here.