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We give a generalization of Thurstons Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences in the deformation space of such a manifold, establishing the existence of compact cores satisfying a certain notion of uniform geometry.
We present an approach for forming sensitivity maps (or sensitivites) using ensembles. The method is an alternative to using an adjoint, which can be very challenging to formulate and also computationally expensive to solve. The main novelties of the
We discuss in this article a property of action of groups by isometries called well displacing. An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. W
In this paper, we investigate representations of links that are either centrally symmetric in $mathbb{R}^3$ or antipodally symmetric in $mathbb{S}^3$. By using the notions of antipodally self-dual and antipodally symmetric maps, introduced and studie
We show that any embedding $mathbb{R}^d to mathbb{R}^{2d+rho(d)-1}$ inscribes a trapezoid or maps three points to a line, where $rho(d)$ denotes the Radon-Hurwitz function. This strengthens earlier results on the nonexistence of affinely $3$-regular
We prove and explore a family of identities relating lengths of curves and orthogeodesics of hyperbolic surfaces. These identities hold over a large space of metrics including ones with hyperbolic cone points, and in particular, show how to extend a