Titlebook: A First Course in Geometric Topology and Differential Geometry; Ethan D. Bloch Textbook 1997 Birkhäuser Boston 1997 Manifold.Topology.alge

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Anatomy of Airways Smooth Muscle,Though our main topic of concern is surfaces, prior to studying smooth surfaces we take a small detour through the study of smooth curves in ℝ. to develop some important tools. Our treatment of curves will be brief; more about curves, including such results such as the pretty Milnor-Fary Theorem, can be found in [M-P] or [DO1].

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Airways Smooth Muscle Cells in Culture,Geodesics are curves in surfaces that play a role analogous to that of straight lines in the plane. Straight lines in the plane have three important properties:

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Assessment and Clinical Patterns,rt off by considering some more general notions concerning the topology of subsets of Euclidean space. In contrast to geometry, which is the study of quantitative properties of spaces, that is, those properties that depend upon measurement (such as length, angle and area), topology is the study of t

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Assessment and Clinical Patterns,ss of geometric objects. One of the most widely studied type of geometric objects are manifolds; the two-dimensional version of a manifold is a surface, which we will define rigorously in the next section.

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Bronchiectasis and Cystic Fibrosis,r proof of the classification of surfaces, as well as for other results, we turn our attention to simplicial surfaces, which are surfaces built out of triangles, and which are much easier to work with than arbitrary surfaces. Examples of simplicial surfaces include the surface of a tetrahedron (a py

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https://doi.org/10.1007/978-3-0348-7558-5functions discussed in Section 4.2. In both cases we define what it means to be “smooth” via parametrizations, define tangent and normal vectors, and then search for geometric quantities such as curvature. There are, however, two fundamental technical differences between surfaces and curves: A surfa

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Karen E. Pedersen,Roy G. GoldieTheorem, essentially the point toward which this entire book has been aimed, shows that these two approaches are deeply related. The simplicial Gauss-Bonnet Theorem (Theorem 3.7.2) has already shown us one connection between a topological invariant (the Euler characteristic) and a geometric quantity

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A First Course in Geometric Topology and Differential Geometry978-0-8176-8122-7Series ISSN 2197-1803 Series E-ISSN 2197-1811