In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.
In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.
undefinedThe book fills a gap existing in the literature. His book covers both theories in an introductory way. It is self-contained. In addition, many detailed and motivational examples are...
Introduces a Morse (index) theory that is easier to use, less technical, and flexible than theories for strongly indefinite functionals. This book presents a self-contained treatment with full proofs...
Meet Tarald, an encumbered yet charismatic hero, and journey with him as he transcends from the mundane to the sublime. During his adventure he will attempt to overthrow a despotic nation, be...
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