Misha Kapovich: Electronic Preprints

Postscript and pdf files of my preprints

3-manifolds, geometric structures, Kleinian groups:

"Hyperbolic manifolds and Discrete Groups. Lectures on Thurston's Hyperbolization". A book which appeared in Birkhauser's Progress in Mathematics in 2001.
"Topological aspects of Kleinian groups in several dimensions". MSRI Preprint, 1992. Updated in 2002.
"Kleinian groups in higher dimensions". (A revised and expanded version of the 2002 preprint. Some of the material of the 2002 version is omitted.) Proceedings of A. Reznikov Memorial Conference "Geometry and Dynamics of Groups and Spaces'', Bonn, September 2006. Birkhauser, Progress in Mathematics, 2007, Vol. 265, p. 485-562.
"On dynamics of pseudo-Anosov homeomorphisms on the representation varieties of surface groups". Ann. Acad. Sci. Fenn., Vol. 23 (1998) p.83-100. Pdf
"Flats in 3-manifolds". Annales de la Faculte des Sciences de Toulouse, Vol. 14 (2005), p. 459-499. Pdf
"On the Ahlfors Finiteness Theorem" , Preprint, 2000. (A simple proof which does not require much analysis.) Pdf
"Deformations of representations of discrete subgroups of SO(3,1)". Math. Annalen, Vol. 299 (1994) p. 341-354. Pdf
"On the deformation theory of representations of fundamental groups of hyperbolic 3-manifolds", (with John Millson). Topology, Vol. 35, N 4 (1996) p. 1085-1106. Pdf
Hyperbolic 4-manifolds fibered over surfaces. Preprint, 1993.
Conformally flat metrics on 4-manifolds. Journal of Differential geometry, 66 (2004), no. 2, p. 289--301.Pdf

Geometrization Conjecture and Ricci Flow. My talk at the MPI Arbeitstagung, 2003. Pdf
Geometrization Theorem. To appear in McGraw Hill 2010 Yearbook of Science & Technology.
Deformation spaces of flat conformal structures, Questions and Answers in General Topology, vol. 8, 1990, p. 253-264.
On the absence of Ahlfors' finiteness theorem for Kleinian groups in dimension 3, (with Leonid Potyagailo) Topology and its Applications, 1991, vol. 40, p. 83-91.
Flat conformal structures on 3-manifolds. Scan of a paper (abut 2/3 of my PhD thesis) which was written in 1990, before I knew how to TeX and how to write.
One of these days it will be converted to TeX and revised (maybe).
Moebius conformal structures on 3-manifolds. Scan of the PhD thesis of my student, Sonjong Hwang, University of Utah, 2002.
Convex projective structures on Gromov-Thurston manifolds, Geometry and Topology, 11 (2007) p. 1777-1830.

Non-coherence of some non-uniform lattices in Isom(Hⁿ), (with Leonid Potyagailo and Ernest Vinberg), Geometry and Topology Monographs (Zieschang's memorial volume), Vol. 14, 2008, p. 335-351.

Homological dimension and critical exponent of Kleinian groups, GAFA, 18 (2009), N 6, 2017-2054.

On sequences of finitely generated discrete groups, Preprint, 2007. To appear in Proceedings of the IV-th Ahlfors-Bers Colloquium.

Introduction to Teichmuller Theory, University of Utah Lecture Notes. Update: August 2008.

Eisenstein series and Dehn surgery, MSRI Preprint, 025-92, 1992.

On absence of Sullivan's cusp finiteness theorem in higher dimensions, In: "Algebra and analysis" (Irkutsk, 1989), p. 77-89. Amer. Math. Soc. Transl. Ser. 2, Vol. 163, Amer. Math. Soc., Providence, RI, 1995.

Linkages, arrangements and algebraic geometry:

"On the moduli spaces of polygons in the Euclidean plane", ( with John Millson). Journal of Differential Geometry, Vol. 42 (1995) N 1, p. 133-164.Pdf

This paper was so good, it was published by the JDG twice: Journal of Differential Geometry, Vol. 42 (1995), N 2, 430-464.

"The symplectic geometry of polygons in the Euclidean space", (with John Millson). Journal of Differential Geometry, Vol. 44 (1996) p. 479-513. Pdf

"On the moduli space of a spherical polygonal linkage", (with John Millson). Canad. Math. Bull., vol. 42 (3), 1999, p. 307-320. Pdf

"Quantization of bending deformations of polygons in E³, hypergeometric integrals and the Gassner representation", ( with John Millson). Canad. Math. Bull., Vol. 44, (2001) p. 36-60. Pdf

"The symplectic geometry of polygons in hyperbolic 3-space" (with John Millson and Thomas Treloar). Asian Journal of Math., vol. 4 (2000), N1 (Kodaira's 75-th birthday volume), p. 123-164.

"Hodge theory and art of paper-folding", (with John Millson). Publications of RIMS, Kyoto, Vol. 33, N 1 (1997) p. 1-33. Pdf

"On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex-algebraic varieties", ( with John Millson). Math. Publications of IHES, vol. 88 (1999), p. 5-95. Pdf

"Moduli Spaces of Linkages and Arrangements", (with John Millson). ``Progress in Geometry'', J.-L. Brylinski, et al (eds.), Progress in Mathematics, Birkhauser, Vol. 172 (1999) p. 237--270. Pdf

"Universality theorems for configuration spaces of planar linkages," (with John Millson). Topology, Vol. 41 (2002), no. 6, p. 1051--1107. Pdf

"On the normal subgroups in the fundamental groups of complex surfaces", Preprint, August 1998. Pdf

"Complex hyperbolic surfaces homotopy-equivalent to a Riemann surface", (with Bill Goldman and Bernhard Leeb). Comm. in Analysis and Geom. , Vol. 9, N 1 (2001), 61-96. Pdf

"On monodromy of Schwarzian differential equation on Riemann surfaces", (with Dan Gallo and Al Marden). Ann. of Math., Vol. 151 (2000), N 2, p. 625-704. Pdf

"Periods of abelian differentials and dynamics", Preprint, April 2000. Pdf

Polygons and their applications to Lie theory:

"Polygons in buildings and their refined side lengths", (with Bernhard Leeb and John Millson), To appear in GAFA.

"Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations", (with Bernhard Leeb and John Millson), JDG, Vol. 81, 2009, p. 297- 354.

"The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra", (with Bernhard Leeb and John Millson), Memoirs of AMS, Vol. 192, 2008.

"A path model for geodesics in Euclidean buildings and its applications to representation theory," (with John Millson), Groups, Geometry and Dynamics, vol 2, 2008, p. 405-480. Pdf

"Structure of the tensor product semigroup," (with John Millson), Asian Math Journal (S.S.Chern memorial issue) Vol. 10, N. 3 (2006) p. 493-540. Pdf

"Generalized triangle inequalities and their applications", - Madrid, August 22-30, 2006. Eds. Marta Sanz-Sola, Javier Soria, Juan L. Varona, Joan Verdera. Vol. 2, p. 719-742.

"The eigencone and Saturation for Spin(8)", (with Shrawan Kumar and John Millson), Pure and Applied Mathematics Quarterly, Vol. 5, N2 (Hirzebruch Special Issue, Part 1), 2009, p. 755-780.

"Verallgemeinerte Dreiecksungleichungen (Generalized Triangle Inequalities)", Jahrbuch of the Max-Planck-Gesellschaft, 2007.
"Affine buildings for dihedral groups", (with Arkady Berenstein), Preprint, 2008.

Geometric group theory:

"On asymptotic cones and quasi-isometry classes of fundamental groups of nonpositively curved manifolds", (with Bernhard Leeb). GAFA, Vol. 5 (1995) N 3, p. 582- 603. Pdf

"Actions of discrete groups on Hadamard spaces," (with Bernhard Leeb). Math. Annalen, Bd. 306 (1996) p. 341-352. Pdf

"Quasi-isometries preserve the geometric decomposition of Haken manifolds", (with Bernhard Leeb). Inventiones Math., Vol. 128, F. 2 (1997), p. 393-416. Pdf

"3-manifold groups and nonpositive curvature," ( with Bernhard Leeb). GAFA, vol. 8 (1998) N 5, p. 841-852. Pdf

"On quasi-isometry invariance of de Rham decomposition of nonpositively curved Riemannian manifolds," (with Bruce Kleiner and Bernhard Leeb). Topology, vol. 37 (1998) N 6, p. 1193-1212. Pdf

"Coarse Alexander duality and duality groups," (with Bruce Kleiner). Journal of Diff. Geometry, 2005, Vol. 69, N. 2, p. 279-352

"Hyperbolic groups with low-dimensional boundary," (with Bruce Kleiner). Ann. Sci. de ENS Paris, t. 33 (2000) p. 647-669.

"Van Kampen's embedding obstruction for discrete groups," (with Mladen Bestvina and Bruce Kleiner). Inventiones Math., Vol. 150 (2002) no. 2, p. 219-235.

"Weak hyperbolization conjecture for 3-dimensional CAT(0) groups," (with Bruce Kleiner). Groups, Geometry and Dynamics, Vol. 1 (2007), p. 67-79.

"Geometry of Gromov-hyperbolic spaces satisfying coarse Poincare duality," (with Bruce Kleiner). Preprint, 2004, preliminary version.

"Geometry of quasi-planes," (with Bruce Kleiner). Preprint, 2004, preliminary version.

"Coarse fibrations and a generalization of the Seifert fibered space conjecture," (with Bruce Kleiner). Preprint, 2004, preliminary version.

"Triangle inequalities in path metric spaces," Geometry and Topology, Vol. 11 (2007) p. 1653-1680.

"Lectures on the Geometric Group Theory," Preliminary version. Spring 2009 revision. Will eventually become a book.

"Energy of harmonic functions and Gromov's proof of Stallings' theorem," Preprint, 2007. Submitted to Communications in Analysis and Geometry.

"Problems on boundaries of groups," List of problems collected at AIM workshop, 2005. Part of Bestvina's list of problems in geometric group theory.
"Arithmetic aspects of self-similar groups," Preprint, 2008.

Maple scripts:

Proof of irredundancy of Belkale-Kumar stability inequalities for SO(8). Maple

Proof of Saturation Theorem for the tensor products of irreducible representations of Spin(8). Maple

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