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New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory by Dan Burghelea (The Ohio State Univ, Usa) at Abbey's Bookshop,
New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory
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Dan Burghelea (The Ohio State Univ, Usa)

New Topological Invariants For Real- And Angle-valued Maps

An Alternative To Morse-novikov Theory

Dan Burghelea (The Ohio State Univ, Usa)

$140.99

Hardback

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English
World Scientific Publishing Co Pte Ltd
16 August 2017
Algebraic topology
This book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse-Novikov theory, referred to in this book as AMN-theory.

These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as 'Lyapunov map' to the topology of the underlying space, in a similar manner as Morse-Novikov theory does.
By:  
Imprint:   World Scientific Publishing Co Pte Ltd
Country of Publication:   Singapore
ISBN:   9789814618243
ISBN 10:   9814618241
Pages:   260
Publication Date:  
Audience:   College/higher education ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
Preliminary Material; Homology/Betti Numbers; Graph Representations; Alexander Function; Invariants for a (Weakly) Tame Map; The Main Results (So Far); Mathematical Implications; Relation with More Sophisticated Mathematics (Constructive Sheafs);

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