Course on Surgery Theory Ams-211

"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." -

Über den Autor / die Autorin

Stanley Chang and Shmuel Weinberger

Zusammenfassung

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 Weinb

Zusatztext

"A valuable source of knowledge (for graduate students and researchers) on surgery theory and its applications."---Krzysztof M. Pawałowski, ZbMATH Open

Produktdetails

• Autoren: Stanley Chang, Shmuel Weinberger, Stanley Weinberger Chang, Chang Stanley, Weinberger Shmuel
• Verlag: Princeton University Press
• Inhalt: Buch
• Produktform: Fester Einband
• Erscheinungsdatum: 31.01.2021
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie
• EAN: 9780691160481
• ISBN: 978-0-691-16048-1
• Anzahl Seiten: 472
• Serie: Annals of Mathematics Studies
• Themen: SCIENCE / Physics / Mathematical & Computational, MATHEMATICS / Geometry / General, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Topology, geometry, Theorem, Calculation, Topology, Manifold, Algebraic Geometry, Linear Algebra, Mathematical physics, Algebraic Topology, Embedding, cohomology, submanifold, singularity theory, vector bundle, Riemannian manifold, fiber bundle, Dirac operator, holonomy, homotopy, Borel conjecture, Cobordism, Novikov conjecture, automorphism, CW Complex, special case, Whitney embedding theorem, differentiable manifold, ring homomorphism, Diagram (category theory), Duality (mathematics), Subgroup, Dimension (vector space), Zariski topology, Isomorphism class, Sheaf (mathematics), Epimorphism, Projection (mathematics), Classifying space, Fundamental group, Hypersurface, Retract, Codimension, Fibration, Scientific notation, Topological space, Characterization (mathematics), Pullback (category theory), Quotient space (topology), Boundary (topology), Homeomorphism, Mapping cylinder, Topological manifold, Transversality (mathematics), Handlebody, Mostow rigidity theorem, Intersection form (4-manifold), Mapping cone (homological algebra), Surgery exact sequence, Whitehead torsion, Exponential map (Riemannian geometry), Surgery theory, Atiyah–Singer index theorem, Hopf Algebra, Lens space, Sard's theorem, Lefschetz fixed-point theorem, Parallelizable manifold, Rokhlin's theorem, Topologist's sine curve, Homotopy lifting property, Lefschetz hyperplane theorem, Category of manifolds