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BRANCHED CAUCHY–RIEMANN STRUCTURES ON ONCE-PUNCTURED TORUS BUNDLES

Published online by Cambridge University Press:  17 May 2019

ALEX CASELLA*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL, USA email [email protected]
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to The University of Sydney in June 2018; degree approved on 28 August 2018; supervisor Stephan Tillmann, auxiliary supervisor Alexander Molev.

References

Agol, I., ‘Ideal triangulations of pseudo-Anosov mapping tori’, in: Topology and Geometry in Dimension Three, Contemporary Mathematics, 560 (American Mathematical Society, Providence, RI, 2011), 117.Google Scholar
Bergeron, N., Falbel, E. and Guilloux, A., ‘Tetrahedra of flags, volume and homology of SL (3)’, Geom. Topol. 18(4) (2014), 19111971.Google Scholar
Casella, A., ‘Branched Cauchy–Riemann structures on once-punctured torus bundles’, Geom. Topol., to appear.Google Scholar
Casella, A., Luo, F. and Tillmann, S., ‘Pseudo-developing maps for ideal triangulations II: positively oriented ideal triangulations of cone-manifolds’, Proc. Amer. Math. Soc. 145(8) (2017), 35433560.Google Scholar
Falbel, E., ‘A spherical CR structure on the complement of the figure eight knot with discrete holonomy’, J. Differential Geom. 79(1) (2008), 69110.Google Scholar
Floyd, W. and Hatcher, A., ‘Incompressible surfaces in punctured-torus bundles’, Topology Appl. 13(3) (1982), 263282.Google Scholar
Fock, V. and Goncharov, A., ‘Moduli spaces of local systems and higher Teichmüller theory’, Publ. Math. Inst. Hautes Études Sci. 1(103) (2006), 1211.Google Scholar
Fock, V. V. and Goncharov, A. B., ‘Moduli spaces of convex projective structures on surfaces’, Adv. Math. 208(1) (2007), 249273.Google Scholar
Garoufalidis, S., Goerner, M. and Zickert, C. K., ‘Gluing equations for PGL (n, C)-representations of 3-manifolds’, Algebr. Geom. Topol. 15(1) (2015), 565622.Google Scholar
Garoufalidis, S., Thurston, D. P. and Zickert, C. K., ‘The complex volume of SL (n, C)-representations of 3-manifolds’, Duke Math. J. 164(11) (2015), 20992160.Google Scholar
Guéritaud, F., ‘On canonical triangulations of once-punctured torus bundles and two-bridge link complements, with an appendix by David Futer’, Geom. Topol. 10 (2006), 12391284.Google Scholar