Author: Ursula LudwigPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Stratified Morse Theory with Tangential Conditions
Author: Ursula LudwigStratified Morse Theory
Author: Mark GoreskyPublisher: Springer Science & Business Media
ISBN: 3642717144
Category : Mathematics
Languages : en
Pages : 279
Book Description
Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.
Stratified Morse Theory
Author: Mark GoreskyPublisher:
ISBN: 9783642717154
Category :
Languages : en
Pages : 292
Book Description
Riemannian Geometry and Geometric Analysis
Author: Jürgen JostPublisher: Springer Science & Business Media
ISBN: 3540288910
Category : Mathematics
Languages : en
Pages : 574
Book Description
Offering some of the topics of contemporary mathematical research, this fourth edition includes a systematic introduction to Kahler geometry and the presentation of additional techniques from geometric analysis.
An Invitation to Morse Theory
Author: Liviu NicolaescuPublisher: Springer Science & Business Media
ISBN: 146141105X
Category : Mathematics
Languages : en
Pages : 366
Book Description
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
Morse Theory: Smooth And Discrete
Author: Kevin P KnudsonPublisher: World Scientific Publishing Company
ISBN: 9814630985
Category : Mathematics
Languages : en
Pages : 196
Book Description
Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.
An Introduction to Morse Theory
Author: Yukio MatsumotoPublisher: American Mathematical Soc.
ISBN: 9780821810224
Category : Mathematics
Languages : en
Pages : 244
Book Description
Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However, finite-dimensional Morse theory has its own significance. This volume explains the finte-dimensional Morse theory.
Morse Theory Under General Boundary Conditions
Author: K. C. ChangMorse Theory
Author: John Willard MilnorPublisher: Princeton University Press
ISBN: 9780691080086
Category : Mathematics
Languages : en
Pages : 166
Book Description
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.' Milnor has published five books with Princeton University Press.
Analytic Combinatorics in Several Variables
Author: Robin PemantlePublisher: Cambridge University Press
ISBN: 1107031575
Category : Mathematics
Languages : en
Pages : 395
Book Description
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.