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Journals and Conferences
We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is quite well-understood, but the topology of the entire space can be quite complicated. However, the topology is wellbehaved at many points in the boundary of AH(M).
We study liftings of holomorphic maps into some Teichmüller spaces. We also study the relationship between universal holomorphic motions and holomorphic lifts into Teichmüller spaces of closed sets in the Riemann sphere.
For a closed subset E of the Riemann sphere, its Teichmüller space TðEÞ is a universal parameter space for holomorphic motions of E over a simply connected complex Banach manifold. In this paper, we study some new applications of this
We study some relationships between holomorphic motions, continuous motions, and monodromy. We also study extensions of holomorphic motions over Riemann surfaces and characterize the extendability of holomorphic motions over some planar regions in terms of monodromy.
We use Earle’s generalization of Montel’s theorem to obtain some results on holomorphic motions over infinite dimensional parameter spaces. We also study some properties of group-equivariant extensions of holomorphic motions.
In this expository note, we discuss the mathematics behind the computer program, SaddleDrop. Based upon ideas of a group at Cornell University, this program draws parameter space pictures for the complex Hénon map. The difficulty of this task is explained as we contrast the well-developed theory of one variable complex dynamics with the two variable Hénon… (More)
We review several applications of Douady-Earle section to holomorphic motions over infinite dimensional parameter spaces. Using DouadyEarle section we study group-equivariant extensions of holomorphic motions. We also discuss the relationship between extending holomorphic motions and lifting holomorphic maps. Finally, we discuss several applications of… (More)
We give an easy description of the barycentric extension of a map of the unit circle to the closed unit disk using some ideas from dynamical systems. We then prove that every circle endomorphism of the unit circle of degree db 2 (with a topological expansion condition) has a conformally natural extension to the closed unit disk which is real analytic on the… (More)
Some Metric Properties of the Teichmüller Space of a Closed Set in the Riemann Sphere by Nishan Chatterjee Advisors: Yunping Jiang and Sudeb Mitra Associated to each closed subset E of the Riemann sphere Ĉ, there is a contractible complex Banach manifold with a basepoint; this was first studied by G. Lieb in his Cornell University doctoral dissertation… (More)