A Course on Surgery Theory
Stanley Chang, Shmuel Weinberger
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
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.
Cobordism, Algebraic closure, Representation theory, Holonomy, Codimension, Atiyah–Hirzebruch spectral sequence, Homeomorphism, Projective module, Hypersurface, Manifold, Obstruction theory, Elliptic operator, Differentiable manifold, Submanifold, Chain complex, Surgery exact sequence, Classifying space, Characteristic class, Rokhlin's theorem, Fundamental group, Homotopy lifting property, Splitting theorem, Subgroup, Isomorphism theorem, Grothendieck group, Atiyah–Singer index theorem, Parallelizable manifold, Topologist's sine curve, Ring homomorphism, Subobject, Cyclic homology, Fiber bundle, Pullback (category theory), Automorphism, Surgery theory, Linear space (geometry), Differential topology, Homology (mathematics), Topological manifold, Classification theorem, Cohomology, Sheaf (mathematics), Euler class, Homotopy, Dimension (vector space), Cofibration, Exponential map (Riemannian geometry), Topology, Geometry, Cohomology ring, Riemannian manifold, Singularity theory, Homotopy group, Isomorphism class, Mapping cylinder, Exterior algebra, Diagram (category theory), Novikov conjecture, Handlebody, CW complex, Theorem, Linear algebra, Category of manifolds, Lefschetz fixed-point theorem, Intersection form (4-manifold), Mostow rigidity theorem, Epimorphism, Whitney embedding theorem, Borel conjecture, Transversality (mathematics), Embedding, Fibration, Moduli space, Sard's theorem, Retract, Mapping cone (homological algebra), Boundary (topology), Topological space, Quotient space (topology), Special case, Quadratic form, Vector bundle, Lefschetz hyperplane theorem, Diffeomorphism, Covering space, Whitehead torsion, Scientific notation, Calculation, Algebraic topology, Hopf algebra, Duality (mathematics), Characterization (mathematics), Dirac operator, Mathematical induction, Basis (linear algebra), Simplicial set, Zariski topology, Compactification (mathematics), Lens space, Projection (mathematics)