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The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induc...
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group An which is not the topological symmetry group of any graph embedded in the manifold. ...
We present a method for generating 2-D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological ch...
We show that Margulis spacetimes without parabolic holonomy are topologically tame. A Margulis spacetime is the quotient of the 3-dimensional Minkowski space by a free proper isometric action of the ...
Let S be a closed oriented surface of genus g > 1 and let ~r denote its fundamental group. Let G be a semisimple Lie group. The purpose of this paper is to investigate the global properties of the s...
The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference inDuluth, 1983, where one of the a...
The number of PL-homeomorphism types of combinatorial manifolds in a fixed dimension with an upper bound on g2 is finite.
One of the foundations of oriented matroid theory is the topological representation theorem of Folkman and Lawrence [8]. It says that an oriented (simple) matroid can be realized uniquely as an arrang...
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we...
Generalized complex geometry and topological sigma-models.
Spatial association rules mining is a process of acquiring information and knowledge from large databases. Due to the nature of geographic space and the complexity of spatial objects and relations, th...
Let M be an n-dimensional submanifold in the simply connected space form Fn+p(c) with c + H2 > 0, where H is the mean curvature of M. We verify that if Mn(n ≥ 3) is an oriented compact submanifold wit...
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at t...

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