Preprints of Brian H. Bowditch

Preprints of Brian H. Bowditch


The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface
Brian H. Bowditch, Makoto Sakuma
August 2016. Abstract.
[Download pdf]

Projections of the sphere graph to the arc graph of a surface
Brian H. Bowditch, Francesca Iezzi
First Draft, December 2015, Revised, July 2016. Abstract.
[Download pdf]

Median and injective metric spaces
Brian H. Bowditch
First draft, November 2015. Revised, March 2016. Abstract.
[Download pdf]

Large-scale rank and rigidity of the Teichmüller metric
Brian H. Bowditch
First draft: March 2015. Revised: March 2016. To appear in J. Topol. Abstract.
[Download pdf]

Large-scale rank and rigidity of the Weil-Petersson metric
Brian H. Bowditch
First draft: March 2015. Revised: December 2015. Abstract.
[Download pdf]

Large-scale rigidity properties of the mapping class groups
Brian H. Bowditch
First draft: March 2015. Revised: April 2016. Abstract.
[Download pdf]

Rigidity of the strongly separating curve graph
Brian H. Bowditch
First draft: June 2014. Revised: April 2016. To appear in Michigan Math. J. Abstract.
[Download pdf]

Quasi-isometric maps between direct products of hyperbolic spaces
Brian H. Bowditch
First draft, April 2014. Revised, March 2016.
Internat. J. Algebra and Computation 26 (2016) 619-633. Abstract.
[Download pdf]

The ending lamination theorem
Brian H. Bowditch
First draft, September 2011. Revised, August 2016 (150 pages) Abstract
[Download pdf] [Previous verstion pdf]
(This uses material from the papers
``Geometric models for hyperbolic 3-manifolds'' and
``End invariants for hyperbolic 3-manifolds''
listed below.)

Coarse hyperbolic models for 3-manifolds
Brian H. Bowditch
September 2010. Abstract.
[Download dvi] [Download pdf (307K)]

Surface group actions and length bounds
Brian H. Bowditch
September 2010. Abstract.
[Download dvi] [Download pdf (349K)]

Train tracks and surface groups acting on hyperbolic spaces
Brian H. Bowditch
September 2010. Abstract.
[Download dvi (70K)] [Download pdf (290K)]

Some properties of median metric spaces
Brian H. Bowditch
First Draft, July 2013, revised January 2015. : Groups, Geom. Dyn. 10 (2016) 279--317. Abstract.
[Download pdf]

Quasiconvexity of bands in hyperbolic 3-manifolds
Brian H. Bowditch
First draft: November 2011. Revised: September 2013 (23 pages). J. Austral. Math. Soc. 96 (2014) 167--185. Abstract.
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One-ended subgroups of mapping class groups
Brian H. Bowditch
First draft: October 2007. Revised: January 2015 (24 pages).
To appear in ``Hyperbolic geometry and geometric group theory'' (eds. K.Fujiwara, S.Kojima, K.Ohshika) Advanced Studies in Pure Mathematics, Mathematical Society of Japan. Abstract.
[Download pdf]

Uniform hyperbolicity of the curve graphs
Brian H. Bowditch
First draft: 11th December 2012. Revised: 24th June 2013. Pacific J. Math. 269 (2014) 269--280. Abstract.
[Download pdf]

Embedding median algebras in products of trees
Brian H. Bowditch
First draft, November 2011. Revised, May 2013. Geom. Dedicata 170 (2014) 157--176. Abstract.
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Stacks of hyperbolic spaces and ends of 3-manifolds
Brian H. Bowditch
February 2002, revised February 2011 (96 pages).
in ``Geometry and Topology Down Under'', Contemporary Mathematics Vol. 597, (eds. C.D.Hodgson, W.H.Jaco, M.G.Scharlemann, S.Tillman) American Mathematical Society (2013) 65--138. Abstract.
[Download pdf (612K)]

Coarse median spaces and groups
Brian H. Bowditch
November 2011. : Pacific J. Math. 261 (2013) 53--93. Abstract.
[Download pdf]

Invariance of coarse median algebras under relative hyperbolicity
Brian H. Bowditch
December 2011. : Math. Proc. Camb. Phil. Soc. 154 (2013) 85--95. Abstract.
[Download pdf]

An upper bound for injectivity radii in convex cores
Brian H. Bowditch
First draft: May 2010. Revised, July 2011 (16 pages). : Groups, Geom. Dyn. 7 (2013) 109--126. Abstract.
[Download pdf (151K)]

Relatively hyperbolic groups
B.H. Bowditch
First draft: July 1997. Revised: September 2011. Internat. J. Algebra and Computation. 22 (2012) 1250016, 66pp. Abstract.
[Download pdf] ([Previous version])

Notes on tameness
Brian H. Bowditch
First draft: June 2006. Revised: November 2009. (45 pages). Enseign. Math. 56 (2010) 229-285. Abstract.
[Download dvi] [Download pdf (389K)]

Atoroidal surface bundles over surfaces
Brian H. Bowditch
First draft: June 2007. Revised: October 2009 (46 pages). Geom. Funct. Anal. 19 (2009) 943-988. Abstract.
[Download dvi] [Download pdf (427K)]

Tight geodesics in the curve complex
Brian H. Bowditch
First draft: October 2003. Revised: November 2003 (16 pages). Invent. Math. 171 (2008) 281-300. Abstract.
[Download dvi] [Download pdf (191K)]

Length bounds on curves arising from tight geodesics
Brian H. Bowditch
First draft: November 2003. Revised: March 2007 (33 pages). Geom. Funct. Anal. 17 (2007) 1001-1042. Abstract.
[Download dvi] [Download pdf (286K)]

Systems of bands in hyperbolic 3-manifolds
Brian H. Bowditch
First draft: October 2003. Revised: February 2007. Pacific J. Math. 232 (2007) 1-42. Abstract.
Text (36 pages). [Download dvi] [Download pdf (284K)]
Figures. First page: [Download pdf (12K)]. Second page: [Download pdf (29K)]

The angel game in the plane
Brian H. Bowditch
First draft: August 2006. Revised: September 2006 (18 pages). Combin. Probab. Comput. 16 (2007) 345-362. Abstract.
[Download dvi] [Download pdf (164K)]

The Cannon-Thurston map for punctured-surface groups
Brian H. Bowditch
First draft: December 2001. Revised: February 2002 (48 pages). Math. Z. 255 (2007) 35-76. Abstract.
[Download dvi]

A course on geometric group theory
Brian H. Bowditch
October 2005. MSJ Mem. Vol 16 (2006). Abstract.
[Download dvi] (65 pages: No pictures!)
[Download pdf (459K)] (72 pages: With pictures.)

Intersection numbers and the hyperbolicity of the curve complex
Brian H. Bowditch
First draft: July 2002. Revised: September 2002 (23 pages). J. reine angew. Math. 598 (2006) 105-129. Abstract.
[Download dvi] [Download pdf (234K)]

Hyperbolic 3-manifolds and the geometry of the curve complex
Brian H. Bowditch
September 2004 (13 pages) : in ``European Congress of Mathematics, Stockholm, June 27 - July 2, 2004'' (ed. A.Laptev) European Mathematical Society Publishing House (2005) 103-115. Abstract.
[Download dvi] [Download pdf (152K)]

Hausdorff dimension and dendritic limit sets
Brian H. Bowditch
January 2003 (8 pages). Math. Annalen 332 (2005) 667-676. Abstract.
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Planar groups and the Seifert conjecture
B.H. Bowditch
First draft: December 1998. Revised: November 1999 (51 pages). J. reine angew. Math. 576 (2004) 11-62. Abstract.
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Groups acting on Cantor sets and the end structure of graphs
B.H. Bowditch
First draft: February 2000. Revised: January 2001 (26 pages). Pacific J. Math. 207 (2002) 31-60. Abstract.
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Splittings of finitely generated groups over two-ended subgroups
B.H. Bowditch
First draft: November 1999. Revised: January 2001 (34 pages). Trans. Amer. Math. Soc. 354 (2002) 1049-1078. Abstract.
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Peripheral splittings of groups
B.H. Bowditch
First draft: January 1998. Revised: January 2001 (28 pages), Trans. Amer. Math. Soc. 353 (2001) 4057-4082. Abstract.
[Download dvi]

Archimedean actions on median pretrees
B.H. Bowditch, J. Crisp
Math. Proc. Camb. Phil. Soc. 130 (2001) 383-400. (17 pages) Abstract.
[Download dvi]

A variation on the unique product property
Brian H. Bowditch
J. London Math. Soc. 62 (2000) 813-826. (15 pages) Abstract.
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Boundaries of geometrically finite groups
B.H. Bowditch
Math. Z. 230 (1999) 509-527. (16 pages) Abstract.
[Download dvi]

Connectedness properties of limit sets
B.H. Bowditch
Trans. Amer. Math. Soc. 351 (1999) 3673-3686. (14 pages) Abstract.
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Treelike structures arising from continua and convergence groups
B.H. Bowditch
Memoirs Amer. Math. Soc. 662 (1999). (85 pages) Abstract.
[Download dvi]

Convergence groups and configuration spaces
B.H. Bowditch
in ``Geometric Group Theory Down Under, proceedings of a Special Year in Geometric Group Theory, Canberra, Australia'' (ed. J.Cossey, C.F.Miller III, W.D.Neumann, M.Shapiro), de Gruyter (1999), 23-54. (31 pages) Abstract.
[Download dvi]

Boundaries of strongly accessible hyperbolic groups
B.H. Bowditch,
revised November 1997
in ``The Epstein Birthday Schrift'', Geometry and Topology Monographs Volume 1, (ed. I.Rivin, C.Rourke, C.Series) International Press (1998) 51-97. (39 pages) Abstract.
[Download dvi]

A topological characterisation of hyperbolic groups
B.H. Bowditch
J. Amer. Math. Soc. 11 (1998) 643-667. (28 pages) Abstract.
[Download dvi]

Group actions on trees and dendrons
B.H. Bowditch
Topology 37 (1998) 1275-1298. (26 pages) Abstract.
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Cut points and canonical splittings of hyperbolic groups
B.H. Bowditch
Acta Math. 180 (1998) 145-186. (38 pages) Abstract.
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Continuously many quasiisometry classes of 2-generator groups
B.H. Bowditch
Comment. Math. Helv. 73 (1998) 232-236. (5 pages) Abstract.
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Spaces of geometrically finite representations
B.H. Bowditch
Ann. Acad. Sci. Fenn. Math. 23 (1998) 389-414. (24 pages) Abstract.
[Download dvi]

Markoff triples and quasifuchsian groups
B.H. Bowditch
Proc. Lond. Math. Soc. 77 (1998) 697-736. (42 pages) Abstract.
[Download dvi]


Scanned preprints:

The following is a preprint version of a published article, now apparently out of print.

Notes on Gromov's hyperbolicity criterion for path-metric spaces
B.H. Bowditch
IHES preprint version, June 1990.
Published version in: ``Group theory from a geometrical viewpoint'' (ed. E.Ghys, A.H aefliger, A.Verjovsky) World Scientific (1991) 64-167. Abstract.
Chapters 0-6. (58 pages)[Scanned pdf (1462K)]
Chapters 7-8. (40 pages)[Scanned pdf (1215K)]

The following is a preprint version of another published article.

Notes on locally CAT(1) spaces
B.H. Bowditch
Aberdeen preprint version, 1992.
Published version in ``Geometric group theory'', (ed. R. Charney, M. Davis, M. Shapiro), de Gruyter (1995) 1-48. Abstract.
Chapters 0-6. (58 pages)[Scanned pdf (1460K)]


Redundant papers:

The following two papers are superseded by ``The ending lamination theorem'' paper, posted above.

End invariants of hyperbolic 3-manifolds
Brian H. Bowditch
December 2005 (32 pages). Abstract.
[Downlo ad dvi] [Download pdf (252K)]

Geometric models for hyperbolic 3-manifolds
Brian H. Bowditch
First draft: August 2005. Revised: October 2006 (81 pages). Abstract.
[Download dvi] [Download pdf (544K)]

The following paper is superseded by `Large-scale rigidity properties of the mapping class groups'' and ``Large-scale rank and rigidity of the Weil-Petersson metric'' posted above.

Rank and rigidity properties of spaces associated to a surface
Brian H. Bowditch
First draft, April 2014. Revised, October 2014. Abstract.
[Download pdf]

The following paper is superseded by: ``Large-scale rank and rigidity of the Teichmüller metric'' posted above.

The coarse geometry of the Teichmüller metric
Brian H. Bowditch
First draft, October 2014. Revised, March 2015. Abstract.
[Download pdf]


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