Lee Mosher

Lecture notes

Mathematical works

Math Reviews of my papers. Requires a subscription to MathSciNet.

Papers and preprints on the math arXiv. Most of these are listed separately below.

Reprints are available for most of the published papers, just ask.
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These works are classified into three groups:

Mapping class groups and dynamics on surfaces

Abstract: These lecture notes present a proof of quasi-isometric rigidity for once punctured mapping class groups, joint work with Kevin Whyte.
Part I, July 5. .pdf preprint
Part II, July 6. .pdf preprint
Part II, July 7. .pdf preprint
Part IV, July 8. .pdf preprint
Abstract: This article, intended for publication in the Proceedings of the 2003 Durham Symposium, expands on the above lecture notes, giving a proof of quasi-isometric rigidity for once punctured mapping class groups, joint work with Kevin Whyte.

Preprint: arXiv math.GR0308065 (last updated 8/7/2003)

Abstract: Let S be a closed, oriented surface of genus at least 2, and consider the extension 1 -> pi_1 S -> MCG(S,p) -> MCG(S) -> 1, where MCG(S) is the mapping class group of S, and MCG(S,p) is the mapping class group of S punctured at p. We prove that any quasi-isometry of MCG(S,p) which coarsely respects the cosets of the normal subgroup pi_1 S is a bounded distance from the left action of some element of MCG(S,p). Combined with recent work of Kevin Whyte this implies that if K is a finitely generated group quasi-isometric to MCG(S,p) then there is a homomorphism K -> MCG(S,p) with finite kernel and finite index image. Our work applies as well to extensions of the form 1 -> pi_1 S -> Gamma_H -> H -> 1, where H is an irreducible subgroup of MCG(S)--we give an algebraic characterization of quasi-isometries of Gamma_H that coarsely respect cosets of pi_1 S.

Preprint: arXiv math.GR/0308067 (last updated 8/7/2003)
Abstract: A splitting sequence of train tracks tau_0 > tau_1 > tau_2 > ... is a train track expansion of a measured foliation F if each train track tau_i carries F. This monograph develops the theory of train track expansions of measured foliations, in parallel with the theory of continued fraction expansions of real numbers. One of the central results describes combinatorial conditions on the sequence that are necessary and sufficient for F to be an arational measured foliation, in parallel with the fact that a continued fraction is irrational if and only if it is infinite. Moreover, if F is arational then tau_0 > tau_1 > tau_2 > ... is an expansion of a unique measured foliation up to topological equivalence, in parallel with the fact that an infinite continued fraction converges to a unique real number. Other results parallel stable equivalence properties of continued fractions. Applications are given to constructions of pseudo-Anosov mapping classes and the classification of pseudo-Anosov mapping classes up to conjugacy. 
In "Geometric and computational perspectives on infinite groups", DIMACS Series 25 (1996), 101--174.
Preprint: arXiv math.GT/9409209 (last updated 9/9/1994)
Annals of Mathematics 142 (1995) no. 2, 303-384.
Research announcement: Math. Res. Lett. 1 (1994) no. 2, 249-255.
Reprint available.
In "Low-dimensional topology and Kleinian groups" (Coventry/Durham, 1984), 13-75, London Math. Soc. Lecture Note Ser., 112, Cambridge Univ. Press, Cambridge, 1986.
Reprint available.
Trans. Amer. Math. Soc. 306 (1988) no. 1, 1-70.
Reprint available.

Geometric group theory

Geometry and Topology 7 (2003) 33-90
Reprint: Geometry and Topology migration to arXiv math.GT/0107035 (last updated 2/2/2003)
Geometry and Topology 6 (2002) 91-152
Reprint: Geometry and Topology migration to arXiv math.GR/0106190 (last updated 4/12/2002)
Geometriae Dedicata 92 (2002) 195-233.
Preprint: arXiv math.GR/0012004 (last updated 2/25/2001)
Annals of Mathematics 158 (2003) 115-164.
Preprint: arXiv math.GR/0010136 (last updated 10/13/2000)
Geometric and Functional Analysis 12 (2002), 915--963.
Preprint: arXiv math.GR/0008215 (last updated 8/29/2000)
Preprint: arXiv math.GR/0005210 (last updated 5/22/2000)
In "Crystallographic groups and their generalizations (Kortrijk, 1999)", 121-134, Contemp. Math., 262, Amer. Math. Soc., Providece, RI, 2002.
Preprint: arXiv math.GR/0005184 (last updated 2/5/2001)
Acta Mathematica 184 (2000), no. 2, 145--202.
Reprint available.
Preprint: arXiv math.GR/0005181 (last updated 5/17/2000)
Inventiones Mathematicae 137 (1999), no. 3, 613--649.
Reprint available.
Preprint: arXiv math.GR/9809010. (last updated 9/2/1998)
Inventiones Mathematicae 131 (1998) no. 2, 419--451.
Reprint available.
Preprint: gzipped postscript (133K).
Proc. AMS 125 (1997) 3447--3455.
Reprint available.
Preprint: gzipped postscript (62K) . (last updated: 12/21/96)
In "Geometric group theory down under (Canberra, 1996)", 225--259, de Gruyter (1999)
Preprint: gzipped postscript (123K). (last updated: 1/22/97)
Comm. Math. Helv. 72 (1997), no. 1, 16--29.
Reprint available.
Preprint: gzipped postscript (67K). (last updated: 4/10/97)
Quarterly Journal of Mathematics 52 (2001) no. 2, 195-216.
Reprint available.
Preprint: gzipped postscript (79K).
Communications in Analysis and Geometry 6 (1998), no. 1, 67--140.
Reprint available.
Preprint: gzipped postscript (221K).
Preprint: gzipped postscript (65K).

Dynamics on 3-manifolds

Preprint: gzipped postscript (812K).
Draft of a monograph about pseudo-Anosov flows on 3-manifolds, and how to construct them using dynamic pairs of branched surfaces.
Topology 40 (2001) no. 3, 503-537.
Reprint available.
Preprint: arXiv math.GT/9507216 (last updated 7/11/1995)
Inventiones Mathematicae 107 (1992) 243--281.
Reprint available.
Duke Mathematical Journal 65, no. 3 (1992) 449--500
Reprint available.
Jour. Differential Geometry 34 (1991) 1--36.
Reprint available.
Ergod. Th. and Dyn. Sys. 9 (1989) no. 2, 329--378.
Correction: Ergod. Th. and Dyn. Sys. 9 (1989) no. 4, 787-791.
Reprint available.