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Topological characterization of canonical Thurston obstructions
1.  Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY 117943660, United States 
References:
[1] 
S. Bonnot, M. Braverman and M. Yampolsky, Thurston equivalence to a rational map is decidable, to appear in Moscow Math. J., (2010). 
[2] 
A. Chéritat, Tan Lei and Shishikura's example of nonmateable degree 3 polynomials without a Levy cycle, to appear in Annales de la faculté des sciences de Toulouse, (2012). 
[3] 
A. Douady and J. H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math., 171 (1993), 263297. doi: 10.1007/BF02392534. 
[4] 
F. R. Gantmacher, "Teoriya Matrits," Second supplemented edition, With an appendix by V. B. Lidskiĭ, Izdat. "Nauka," Moscow, 1966. 
[5] 
J. H. Hubbard, "Teichmüller Theory and Applications to Geometry, Topology, and Dynamics. Vol. 1. Teichmüller Theory," With contributions by Adrien Douady, William Dunbar, Roland Roeder, Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska and Sudeb Mitra, With forewords by William Thurston and Clifford Earle, Matrix Editions, Ithaca, NY, 2006. 
[6] 
Y. Imayoshi and M. Taniguchi, "An Introduction to Teichmüller Spaces," Translated and revised from the Japanese by the authors, SpringerVerlag, Tokyo, 1992. doi: 10.1007/9784431681748. 
[7] 
O. Lehto and K. I. Virtanen, "Quasiconformal Mappings in the Plane," Second edition, Translated from the German by K. W. Lucas, Die Grundlehren der mathematischen Wissenschaften, Band 126, SpringerVerlag, New York, 1973. 
[8] 
C. T. McMullen, "Complex Dynamics and Renormalization," Annals of Mathematics Studies, 135, Princeton University Press, Princeton, NJ, 1994. 
[9] 
J. Milnor, "Dynamics in One Complex Variable," Third edition, Annals of Mathematics Studies, 160, Princeton University Press, Princeton, NJ, 2006. 
[10] 
_____, On Lattès maps, in "Dynamics on the Riemann Sphere," Eur. Math. Soc., Zürich, (2006), 943. 
[11] 
K. M. Pilgrim, Canonical Thurston obstructions, Adv. Math., 158 (2001), 154168. doi: 10.1006/aima.2000.1971. 
[12] 
_____, "Combinations of Complex Dynamical Systems," Lecture Notes in Mathematics, 1827, SpringerVerlag, Berlin, 2003. 
[13] 
N. Selinger, "On Thurston's Characterization Theorem for Branched Covers," Ph.D Thesis, 2011. 
[14] 
_____, Thurston's pullback map on the augmented Teichmüller space and applications, Inventiones Mathematicae, 189 (2012), 111142. 
[15] 
S. A. Wolpert, Geometry of the WeilPetersson completion of Teichmüller space, in "Surveys in Differential Geometry, Vol. VIII" (Boston, MA, 2002), Surv. Differ. Geom., VIII, Int. Press, Somerville, MA, (2003), 357393. 
[16] 
_____, The WeilPetersson metric geometry, in "Handbook of Teichmüller Theory, Vol. II," IRMA Lect. Math. Theor. Phys., 13, Eur. Math. Soc., Zürich, (2009), 4764. 
show all references
References:
[1] 
S. Bonnot, M. Braverman and M. Yampolsky, Thurston equivalence to a rational map is decidable, to appear in Moscow Math. J., (2010). 
[2] 
A. Chéritat, Tan Lei and Shishikura's example of nonmateable degree 3 polynomials without a Levy cycle, to appear in Annales de la faculté des sciences de Toulouse, (2012). 
[3] 
A. Douady and J. H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math., 171 (1993), 263297. doi: 10.1007/BF02392534. 
[4] 
F. R. Gantmacher, "Teoriya Matrits," Second supplemented edition, With an appendix by V. B. Lidskiĭ, Izdat. "Nauka," Moscow, 1966. 
[5] 
J. H. Hubbard, "Teichmüller Theory and Applications to Geometry, Topology, and Dynamics. Vol. 1. Teichmüller Theory," With contributions by Adrien Douady, William Dunbar, Roland Roeder, Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska and Sudeb Mitra, With forewords by William Thurston and Clifford Earle, Matrix Editions, Ithaca, NY, 2006. 
[6] 
Y. Imayoshi and M. Taniguchi, "An Introduction to Teichmüller Spaces," Translated and revised from the Japanese by the authors, SpringerVerlag, Tokyo, 1992. doi: 10.1007/9784431681748. 
[7] 
O. Lehto and K. I. Virtanen, "Quasiconformal Mappings in the Plane," Second edition, Translated from the German by K. W. Lucas, Die Grundlehren der mathematischen Wissenschaften, Band 126, SpringerVerlag, New York, 1973. 
[8] 
C. T. McMullen, "Complex Dynamics and Renormalization," Annals of Mathematics Studies, 135, Princeton University Press, Princeton, NJ, 1994. 
[9] 
J. Milnor, "Dynamics in One Complex Variable," Third edition, Annals of Mathematics Studies, 160, Princeton University Press, Princeton, NJ, 2006. 
[10] 
_____, On Lattès maps, in "Dynamics on the Riemann Sphere," Eur. Math. Soc., Zürich, (2006), 943. 
[11] 
K. M. Pilgrim, Canonical Thurston obstructions, Adv. Math., 158 (2001), 154168. doi: 10.1006/aima.2000.1971. 
[12] 
_____, "Combinations of Complex Dynamical Systems," Lecture Notes in Mathematics, 1827, SpringerVerlag, Berlin, 2003. 
[13] 
N. Selinger, "On Thurston's Characterization Theorem for Branched Covers," Ph.D Thesis, 2011. 
[14] 
_____, Thurston's pullback map on the augmented Teichmüller space and applications, Inventiones Mathematicae, 189 (2012), 111142. 
[15] 
S. A. Wolpert, Geometry of the WeilPetersson completion of Teichmüller space, in "Surveys in Differential Geometry, Vol. VIII" (Boston, MA, 2002), Surv. Differ. Geom., VIII, Int. Press, Somerville, MA, (2003), 357393. 
[16] 
_____, The WeilPetersson metric geometry, in "Handbook of Teichmüller Theory, Vol. II," IRMA Lect. Math. Theor. Phys., 13, Eur. Math. Soc., Zürich, (2009), 4764. 
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