A Course on Surgery Theory (eBook)

Stanley Chang, Shmuel Weinberger (Autoren)

eBook Download: PDF

2021
472 Seiten
Princeton University Press (Verlag)
978-0-691-20035-4 (ISBN)

Infos

An advanced treatment of surgery theory for graduate students and researchersSurgery 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.

Produkt-Details

• Erscheint lt. Verlag: 26.1.2021
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 14 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: algebraic closure • algebraic topology • assembly map • assembly perspective on surgery • Atiyah–Hirzebruch spectral sequence • Atiyah–Singer index theorem • automorphism • Basis (linear algebra) • Borel conjecture • Boundary (topology) • Bounded Topology • Calculation • Category of manifolds • chain complex • Chapman-Ferry • Characteristic class • Characterization (mathematics) • Classification of manifolds • Classification theorem • classifying space • Cobordism • Codimension • cofibration • cohomology • Cohomology ring • Compactification (mathematics) • controlled topology • Covering space • CW complex • cyclic homology • Diagram (category theory) • diffeomorphism • differentiable manifold • Differential topology • Dimension (vector space) • Dirac Operator • Duality (mathematics) • elliptic operator • Embedding • Epimorphism • Euler class • Exponential map (Riemannian geometry) • Exterior algebra • Farrell-Hsiang • fiber bundle • fibration • flat manifolds • fundamental group • Geometry • Grothendieck group • Handlebody • holonomy • Homeomorphism • homology manifolds • Homology (mathematics) • homology surgery • Homotopy • Homotopy group • homotopy invariant • Homotopy lifting property • homotopy theory • Hopf algebra • hypersurface • index theorem • induction theory • Intersection form (4-manifold) • isomorphism class • Isomorphism Theorem • Kirby-Siebenmann • Lefschetz fixed-point theorem • Lefschetz hyperplane theorem • Lens space • linear algebra • Linear space (geometry) • L-theory • manifold • manifold theory • Mapping cone (homological algebra) • mapping cylinder • Mathematical Induction • moduli space • Mostow rigidity theorem • Novikov conjecture • Obstruction theory • Parallelizable manifold • PL category • PL topology • Projection (mathematics) • projective module • Pullback (category theory) • quadratic form • quadratic form theory • Quotient space (topology) • Representation Theory • Retract • Riemannian manifold • ring homomorphism • Rokhlin's theorem • Sard's theorem • scientific notation • Sheaf (mathematics) • simplicial set • singularity theory • smooth category • Special case • Splitting theorem • splitting theorems • Stratified Spaces • SUBGROUP • submanifold • Subobject • surgery exact sequence • surgery obstruction group • Surgery theory • tangent bundle • Theorem • topological category • Topological Manifold • Topological space • topological surgery theory • Topologist's sine curve • Topology • Transversality (mathematics) • vector bundle • Whitehead torsion • Whitney embedding theorem • Zariski topology
• ISBN-10: 0-691-20035-1 / 0691200351
• ISBN-13: 978-0-691-20035-4 / 9780691200354