Leseprobe
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A Course on Surgery Theory
Stanley Chang, Shmuel Weinberger
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
An advanced treatment of surgery theory for graduate students and researchers
Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, A Course on Surgery Theory serves as an important resource for the mathematics community.
Kundenbewertungen
Topological manifold, Calculation, Mapping cone (homological algebra), Submanifold, Homotopy, Fibration, Fiber bundle, Mapping cylinder, Embedding, Handlebody, Intersection form (4-manifold), Retract, Surgery exact sequence, Novikov conjecture, Dimension (vector space), Projection (mathematics), Automorphism, Classifying space, Differentiable manifold, Manifold, Borel conjecture, Topology, Mostow rigidity theorem, Riemannian manifold, Category of manifolds, Homeomorphism, Sheaf (mathematics), Scientific notation, Diagram (category theory), Topologist's sine curve, CW complex, Fundamental group, Parallelizable manifold, Whitney embedding theorem, Theorem, Quotient space (topology), Algebraic topology, Pullback (category theory), Hypersurface, Lefschetz hyperplane theorem, Lens space, Characterization (mathematics), Transversality (mathematics), Cobordism, Special case, Homotopy lifting property, Cohomology, Dirac operator, Epimorphism, Hopf algebra, Ring homomorphism, Topological space, Exponential map (Riemannian geometry), Codimension, Holonomy, Boundary (topology), Duality (mathematics), Subgroup, Singularity theory, Sard's theorem, Vector bundle, Isomorphism class, Lefschetz fixed-point theorem, Geometry, Atiyah–Singer index theorem, Linear algebra, Whitehead torsion, Rokhlin's theorem, Zariski topology, Surgery theory