Homotopy Fibrations With A Section After Looping
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Homotopy Fibrations with a Section After Looping
We analyze a general family of fibrations which, after looping, have sections. Methods are developed to determine the homotopy type of the fibre and the homotopy classes of the map from the fibre to the base. The methods are driven by applications to two-cones, Poincaré Duality complexes, the connected sum operation, and polyhedral products.
Homotopy Fibrations with a Section after Looping
Author: Stephen Theriault
language: en
Publisher: American Mathematical Society
Release Date: 2024-08-19
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Lusternik-Schnirelmann Category
Author: Octavian Cornea
language: en
Publisher: American Mathematical Soc.
Release Date: 2003
''Lusternik-Schnirelmann category is like a Picasso painting. Looking at category from different perspectives produces completely different impressions of category's beauty and applicability.'' --from the Introduction Lusternik-Schnirelmann category is a subject with ties to both algebraic topology and dynamical systems. The authors take LS-category as the central theme, and then develop topics in topology and dynamics around it. Included are exercises and many examples. The book presents the material in a rich, expository style. The book provides a unified approach to LS-category, including foundational material on homotopy theoretic aspects, the Lusternik-Schnirelmann theorem on critical points, and more advanced topics such as Hopf invariants, the construction of functions with few critical points, connections with symplectic geometry, the complexity of algorithms, and category of $3$-manifolds. This is the first book to synthesize these topics. It takes readers from the very basics of the subject to the state of the art. Prerequisites are few: two semesters of algebraic topology and, perhaps, differential topology. It is suitable for graduate students and researchers interested