Lusternik-Schnirelmann Category

Lusternik-Schnirelmann Category PDF

Author: Octavian Cornea

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 352

ISBN-13: 0821834045

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''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

Lusternik-Schnirelmann Category and Related Topics

Lusternik-Schnirelmann Category and Related Topics PDF

Author: Octavian Cornea

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 218

ISBN-13: 0821828002

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This collection is the proceedings volume for the AMS-IMS-SIAM Joint Summer Research Conference, Lusternik-Schnirelmann Category, held in 2001 at Mount Holyoke College in Massachusetts. The conference attracted an international group of 37 participants that included many leading experts. The contributions included here represent some of the field's most able practitioners. With a surge of recent activity, exciting advances have been made in this field, including the resolution of several long-standing conjectures. Lusternik-Schnirelmann category is a numerical homotopy invariant that also provides a lower bound for the number of critical points of a smooth function on a manifold. The study of this invariant, together with related notions, forms a subject lying on the boundary between homotopy theory and critical point theory. These articles cover a wide range of topics: from a focus on concrete computations and applications to more abstract extensions of the fundamental ideas. The volume includes a survey article by P. Hilton that discusses earlier results from homotopy theory that form the basis for more recent work in this area. In this volume, professional mathematicians in topology and dynamical systems as well as graduate students will catch glimpses of the most recent views of the subject.

Lusternik-Schnirelmann Category

Lusternik-Schnirelmann Category PDF

Author: Octav (Universit De Montreal Cornea

Publisher: American Mathematical Society(RI)

Published: 2014-05-21

Total Pages: 352

ISBN-13: 9781470413309

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''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

Lusternik-Schnirelmann Category

Lusternik-Schnirelmann Category PDF

Author: Octavian Cornea

Publisher: American Mathematical Soc.

Published:

Total Pages: 354

ISBN-13: 9780821875155

DOWNLOAD EBOOK →

Lusternik-Schnirelmann category is a subject with ties to both algebraic topology and dynamical systems. This book provides a unified approach to LS-category, including foundational material on homotopy theoretic aspects of the subject, 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 which takes LS-category as its central theme and develops topics in topology and dynamics around it. As such, it leads from the very basics of the subject to the present-day state of the art. The prerequisites for reading the book are few: two semesters of algebraic topology and, perhaps, differential topology.

On Lusternik-Schnirelmann Category of Connected Sums

On Lusternik-Schnirelmann Category of Connected Sums PDF

Author: Robert J. Newton

Publisher:

Published: 2013

Total Pages: 24

ISBN-13:

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This dissertation uses techniques from algebraic topology to place bounds on the Lusternik-Schnirelmann category of a quotient space with sufficient conditions. The first chapter contains a quick summary on the origins of the theory and some mention on current activity within the field. The second chapter provides the definitions and constructions used in this study. There will be examples of the Lusternik-Schnirelmann category for some basic spaces. The techniques from algebraic topology that are used will be discussed here. The chapter concludes with some integration of the algebera and topology. In the third chapter we get to the main ideas in this dissertation. We prove the main theorem and describe some very quick results that follow from the theorem. The dissertation concludes with ideas for future work.

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