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
- Homology and dynamics in quasi-isometric rigidity
Abstract: These lecture notes present a
proof of quasi-isometric rigidity for once punctured mapping class
groups, joint work with Kevin Whyte.
- Lecture Notes, Durham, July 5-8, 2003
- Homology and dynamics in quasi-isometric rigidity of
once-punctured mapping class groups
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)
- Fiber respecting quasi-isometries of surface group extensions
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)
- Train track expansions of measured foliations
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.
- Version 2/15/2003, 297 pages, .pdf
preprint
- Version 12/29/2003, 354 pages, .pdf
preprint
- This version contains, in very rough draft, applications to
enumeration of pseudo-Anosov conjugacy classes, and to the conjugacy
problem in the mapping class group.
- A user's guide to the mapping class group: once-punctured
surfaces
In "Geometric and computational
perspectives on infinite groups",
DIMACS Series 25 (1996), 101--174.
Preprint:
arXiv math.GT/9409209 (last updated 9/9/1994)
- Mapping class groups are automatic
Annals of Mathematics 142 (1995) no. 2,
303-384.
Research announcement: Math. Res. Lett. 1 (1994) no. 2, 249-255.
Reprint
available.
- The classification of pseudo-Anosovs
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.
- Tiling the projective foliation space of a punctured surface
Geometric group theory
- Stable Teichmuller quasigeodesics and ending laminations
- Convex cocompact subgroups of mapping class groups -
joint with B. Farb
- Maximally symmetric trees -
joint with M. Sageev and K. Whyte
- Quasi-actions on trees I: Bounded valence -
joint with M. Sageev and K. Whyte
- The geometry of surface-by-free groups
- joint with B. Farb
Geometric and Functional Analysis 12
(2002), 915--963.
Preprint:
arXiv
math.GR/0008215
(last updated 8/29/2000)
- Quasi-actions on trees: research announcement -
joint with M. Sageev and K. Whyte
- Problems on the geometry of finitely generated solvable
groups - joint with B. Farb.
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)
- On the asymptotic geometry of abelian-by-cyclic groups,-
joint with B. Farb.
- Quasi-isometric rigidity for the solvable Baumslag-Solitar
groups, II - joint with Benson Farb.
- A rigidity theorem for the solvable Baumslag-Solitar groups
- joint with B. Farb, appendix by D. Cooper.
- A hyperbolic-by-hyperbolic hyperbolic group.
- Indiscrete representations, laminations, and tilings.
In "Geometric group theory down under
(Canberra, 1996)", 225--259, de Gruyter (1999)
Preprint:
gzipped
postscript (123K). (last updated: 1/22/97)
- Central quotients of biautomatic groups.
- Two-dimensional measured laminations of positive Euler
characteristic
- joint with U. Oertel.
- Spaces which are not negatively curved
- joint with U. Oertel.
- Nonmanifold hyperbolic groups of high cohomological dimension
- joint with M. Sageev.
Dynamics on 3-manifolds
- Laminations and flows transverse to finite depth
foliations,
Part I: Branched surfaces and dynamics.
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.
- Quasigeodesic flows in hyperbolic three-manifolds,
joint with Sergio Fenley.
- Dynamical systems and the homology norm of a 3-manifold II
- Dynamical systems and the homology norm of a 3-manifold, I:
Efficient intersection of surfaces and flows
- Surfaces and branched surfaces transverse to pseudo-Anosov
flows on 3-manifolds
- Equivariant spectral decomposition for flows with a Z-action
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.