Simplifying spines of 3-manifolds
نویسندگان
چکیده
منابع مشابه
Convexity of Morse Stratifications and Gradient Spines of 3-manifolds
We notice that a generic nonsingular gradient field v = ∇f on a compact 3-fold X with boundary canonically generates a simple spine K(f, v) of X. We study the transformations of K(f, v) that are induced by deformations of the data (f, v). We link the Matveev complexity c(X) of X with counting the double-tangent trajectories of the v-flow, i.e. the trajectories that are tangent to the boundary ∂...
متن کاملConvexity of Morse Stratifications and Spines of 3-manifolds
The gradient fields v of nonsingular functions f on compact 3folds X with boundary are used to generate their spines K(f, v). We study the transformations of K(f, v) that are induced by deformations of the data (f, v). We link the Matveev complexity of c(X) with counting the trajectories of the v-flow that are tangent to the boundary ∂X at a pair of distinct points (call them double-tangent tra...
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Continuing after the previous papers of this series, attention is devoted to RR-systems having two towns (i.e., to compact 3-manifolds with spines corresponding to group presentations having two generators). An interesting kind of symmetry is noted and then used to derive some useful results. Specifically, the following theorems are proved: Theorem 1. Let tf> be a group presentation correspondi...
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We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubblemoves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.
متن کاملBranched Spines and Contact Structures on 3-manifolds
The study of the characteristic foliation induced on an embedded surface is one of the main themes in 3-dimensional contact topology. In particular (see [10]) one can describe exactly what foliations arise (“existence results”). Moreover one knows that the characteristic foliation F = Fξ(Σ) determines uniquely the contact structure ξ in a neighbourhood of a surface Σ (“uniqueness results”). (By...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1978
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1978.74.473