Recent Updates

• 6-19-2006. Updated thesis with its final accepted form.
• 6-19-2006. Updated "Arithmetic lattices in SU(n,1)". Minor changes. I hope to post a substantially revised version before the end of the summer.
  
• 6-13-2006. Posted "Length equivalent hyperbolic manifolds" with Chris Leininger and Alan Reid.
  
• 6-9-2006. Listed project with Ruth Gornet on simple length spectra.
  
• 6-9-2006. Updated "Arithmetic cusp shapes are dense". This article will be submitted in a few days.
  
• 6-9-2006. Updated "Constructing isospectral manifolds". This article will be submitted in a few days.
  
• 5-19-2006. Updated "Arithmetic cusp shapes are dense". The most dramatic changes took place in the introduction.
  
• 5-11-2006. In "Fully residually free aspherical Kahler groups are Fuchsian" ignore the comment about the intersection of two cut groups being a cut group. This is incorrect; I thank Graham Niblo for pointing this out.
  
• 5-11-2006. "Length equivalent hyperbolic manifolds" with Chris Leininger and Alan Reid is listed. I suspect a version will appear here within a month.
  
• 5-2-2006. I successfully defended my thesis. The final version will be posted soon.
  
• 4-3-2006. "Constructing isospectral manifolds" updated. A fairly serious error was found in the previous version and subsequently fixed. Another update is likely to follow in the next few weeks to clean up this newest version.
  
• 3-28-2006. "Separable subgroups of the mapping class groups" with Chris Leininger accepted for publication in Topology and its Applications.
  
• 3-16-2006. Fixed some errors in "Arithmetic cusp shapes are dense".
  
• 3-13-2006. Updated "Separable subgroups of the mapping class groups" with Chris Leininger. Very minor changes.
• 3-13-2006. "Finite subgroups of arithmetic lattices in U(2,1)" accepted in Geometriae Dedicata volume for Crystallographic groups and their generalisations IV.

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Papers and projects

	Title	Authors	Status and measurements	Files
(1)	Peripheral separability and cusps of arithmetic hyperbolic orbifolds.		Algebr. and Geom. Topol. 2004 (4), 721-755. See web site.
(2)	Finite subgroups of arithmetic lattices in U(2,1).		To appear in Geom. Dedicata.
(3)	Separable subgroups of the mapping class groups (with  C. J. Leininger)		To appear in Topology Appl.
(4)	Cusps of Hilbert modular varieties.		Submitted. (17 pages, 6-14-2005)
(5)	Arithmetic cusp shapes are dense.		Submitted. (10 pages, 6-15-2006)
(6)	Constructing isospectral manifolds.		Submitted. (39 pages, 6-16-2006)
(7)	Length equivalent hyperbolic manifolds (with C. J. Leininger and A. W. Reid)		Submitted. (12 pages, 6-13-2006)
(8)	Geodesic submanifolds of rank-1 arithmetic manifolds		In preparation.  (25 pages, 2-16-2006)
(9)	Finite subgroups of lattices and the finite cyclic property.		In preparation.  (13 pages, 2-06-2006).
(10)	Locally symmetric manifolds and simple geodesics (with A. W. Reid).		In progress/preparation. (9 pages, 11-30-2005).
(11)	Symmetries of flat manifolds  (with Y. Kamishima ).		In progress/preparation. (3 pages, 2-16-2006).
(12)	The simple length spectrum is unbounded (with R. Gornet)		In progress/preparation. (8 pages, 6-09-2006)
	Simple geodesics and surfaces (with C. J. Leininger).		In progress. (6 pages, 11-30-2005).
	Asymptotic properties of geodesics on surfaces (with B. Farb).		In progress. (4 pages, 11-30-2005).
	Arithmetic lattices in reductive groups  (with B. Farb).		In progress. (11-30-2005)

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Thesis and books

(*)	Cusps of arithmetic orbifolds. Ph.D. thesis.	Second draft.  (110 pages, 6-19-2006).
(1)	Arithmetic lattices in SU(n,1).	Working partial draft. (79 page mongraph, 6-19-2006)

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Notes to never appear in print

These notes are not suited for general public consumption and consequently the reader should proceed with care!!!

All nil 3-manifolds are cusps of complex 2-orbifolds.	Pre-never-print. (19 pages)
A generalization of Long's verbal lemma; don't look too closely at this.	Pre-pre-never-print. (4 pages)
Scheme automorphism groups.	In preparation.
Polycyclic subgroup separability in scheme automorphism groups (with C. J. Leininger) .	In preparation.
Fully residually free aspherical Kahler groups are Fuchsian.	Pre-pre-never-print. (4 pages)
Limit groups are omnipotent (with B. Klaff).	In preparation (5 pages).
A note on Guy's conjecture.	In preparation; maybe.

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