미분위상수학

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말뭉치

  1. In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.[1]
  2. Differential topology considers the properties and structures that require only a smooth structure on a manifold to be defined.[1]
  3. Smooth manifolds are 'softer' than manifolds with extra geometric structures, which can act as obstructions to certain types of equivalences and deformations that exist in differential topology.[1]
  4. Differential topology and differential geometry are first characterized by their similarity.[1]
  5. ’s course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others.[2]
  6. In this 2h-per-week lecture course we will cover the foundations of differential topology, which are often assumed to be known in more advanced classes in geometry, topology and related fields.[3]
  7. In my own case it has come to pass that over the (by now, long) years, algebraic and differential topology have been on the ascendant.[4]
  8. The study of differential topology stands between algebraic geometry and combinatorial topology.[4]
  9. Differential Topology of central importance in Mathematics and required background for every research mathematician and theoretical physicist.[5]
  10. The aim of the course is to introduce fundamental concepts and examples in differential topology.[6]
  11. Important general mathematical concepts were developed in differential topology.[7]
  12. A separate branch of differential topology, related to the calculus of variations, is the global theory of extremals of various functionals on manifolds of geodesics.[7]
  13. The interest on the part of modern physics in the methods of differential topology greatly increased in the 1970s.[7]
  14. Our expertise in differential topology lies in the differential topology of infinite dimensional spaces.[8]
  15. This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools.[9]
  16. As a general rule, anything that requires a Riemannian metric is part of differential geometry, while anything that can be done with just a differentiable structure is part of differential topology.[10]
  17. For example, the classification of smooth manifolds up to diffeomorphism is part of differential topology, while anything that involves curvature would be part of differential geometry.[10]
  18. Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field.[11]
  19. Milnor's classic book "Topology from the Differentiable Viewpoint" is a terrific introduction to differential topology as covered in Chapter 1 of the Part II course.[12]
  20. Differential topology is a subject in which geometry and analysis are used to obtain topological invariants of spaces, often numerical.[13]
  21. In differential topology we count the number of zeros of a smooth vector field, weighted by their indices, and once again get two.[13]
  22. The kinds of questions that one asks in differential topology are therefore global.[13]
  23. Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds.[14]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Differential topology
  2. ↑ Elements of Differential Topology
  3. ↑ Lecture Course "Differential Topology"
  4. ↑ 4.0 4.1 Mathematical Association of America
  5. ↑ Differential Topology
  6. ↑ Differential Topology
  7. ↑ 7.0 7.1 7.2 Encyclopedia of Mathematics
  8. ↑ Department of Mathematics, Faculty of Sciences, Vrije Universiteit Amsterdam
  9. ↑ Differential Topology
  10. ↑ 10.0 10.1 Differential topology versus differential geometry
  11. ↑ Differential Topology | Geometry and topology
  12. ↑ Differential Geometry and Topology
  13. ↑ 13.0 13.1 13.2 Differential topology
  14. ↑ AMS eBooks: AMS Chelsea Publishing

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  • [{'LOWER': 'differential'}, {'LEMMA': 'topology'}]
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