Topology (from the Greek t?p??, “place”, and ?????, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation.
Supplemental catalog subcollection information: American Libraries Collection; American University Library Collection; Historical Literature; Bibliography: l. 40-41
Supplemental catalog subcollection information: American Libraries Collection; American University Library Collection; Historical Literature; Rare book preservation notes: Due to the deteriorated condition of this book, there were limitations with the dig
Supplemental catalog subcollection information: American Libraries Collection; Historical Literature; Manuscript copy; Thesis - University of Florida; Vita; Bibliography: leaves 67-68
Manuscript copy; Thesis - University of Florida; Vita; Bibliography: leaves 67-68
Description: First part of this course note presents a rapid overview of metric spaces to set the scene for the main topic of topological spaces.Further it covers metric spaces, Continuity and open sets for metric spaces, Closed sets for metric spaces, Topological spaces, Interior and closure, More on topological structures, Hausdorff spaces and Compactness.
Description: We will follow a direct approach to differential topology and to many of its applications without requiring and exploiting the abstract machinery of algebraic topology. The course will cover immersion, submersions and embeddings of manifolds in Euclidean space (including the basic results by Sard and Whitney), a discussion of the Euler number and winding numbers, fixed point theorems, the Borsuk-Ulam theorem and respective applications. At the end of the cou...
Description: There are two reasons why this may be a useful exercise. First, it may help to show K-theorists brought up in the \algebraic school how their subject is related to topology. And secondly, clarifying the relationship between K- theory and topology may help topologists to extract from the wide body of K-theoretic literature the things they need to know to solve geometric problems
Description: This lecture note explains everything about Algebraic Topology.
Description: The seminal `MIT notes' of Dennis Sullivan were issued in June 970 and were widely circulated at the time. The notes had a ma- or in°uence on the development of both algebraic and geometric topology, pioneering
Description: This note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.
Description: This note provides an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible to participants with little or no prior knowledge of the subject.
Description: This is one day going to be a textbook on K-theory, with a particular emphasis on connections with geometric phenomena like intersection multiplicities.
Description: This note covers the following topics: Geometric reformulation, The Adams-Novikov spectral sequence, Elliptic cohomology, What is TMF, Geometric and Physical Aspect.
Description: This book covers the following topics: Cell complexes and simplical complexes, fundamental group, covering spaces and fundamental group, categories and functors, homological algebra, singular homology, simplical and cellular homology, applications of homology.