7 edition of **Circle-Valued Morse Theory (de Gruyter Studies in Mathematics 32) (De Gruyter Studies in Mathematics)** found in the catalog.

- 150 Want to read
- 40 Currently reading

Published
**December 30, 2006**
by Walter de Gruyter
.

Written in English

- Differential & Riemannian geometry,
- Mathematics,
- Science/Mathematics,
- Advanced,
- Geometry - General

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 454 |

ID Numbers | |

Open Library | OL9017198M |

ISBN 10 | 3110158078 |

ISBN 10 | 9783110158076 |

Clay Mathematics Institute Summer School Alfréd Rényi Institute of Mathematics Budapest, Hungary Circle Valued Morse Theory for Knots and Links 71 Hiroshi Goda Floer Homologies and Contact Structures Lectures on Open Book Decompositions and Contact Structures John B. Etnyre Contact Surgery and Heegaard Floer Theory File Size: 3MB. The basic Morse theory gives a relationship of a Morse map and a h andle de-composition for a manifold. In this section, we review the no tion of Heegaard split-ting for sutured manifold introduced in [7] and [8], and reve al the relationship with circle-valued Morse maps. Moreover, we present some properti es which are used to.

The present book is divided into three conceptually distinct parts. In the rst part we lay the foundations of Morse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard{Lefschetz theory. Let X be a closed manifold with χ (X) = 0, and let f: X → S 1 be a circle-valued Morse function. We define an invariant I which counts closed orbits of the gradient of f, together with flow lines between the critical show that our invariant equals a form of topological Reidemeister torsion defined by Turaev [Math. Res. Lett. 4 () –].Cited by:

(ebook) Circle-valued Morse Theory () from Dymocks online store. In the early s M. Morse discovered that the number of. 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 s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in.

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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 by: The central geometrical construction of the circle-valued Morse theory is the Novikov complex, introduced by Novikov in.

It is a generalization to the circle-valued case of its classical predecessor — the Morse complex. Our approach to the subject is based on this construction. This became a starting point of the Morse theory which is now one of the basic parts of differential topology.

Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. Novikov in the early s. Circle-valued Morse theory. From Wikipedia, the free encyclopedia. Jump to navigation Jump to search. In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology.

It is an important special case of Sergei Novikov 's Morse theory of closed one-forms. Let X be a closed manifold with zero Euler characteristic, and let f: X --> S^1 be a circle-valued Morse function.

We define an invariant I which counts closed orbits of the gradient of f, together with flow lines between the critical points. We develop the real-valued and circle-valued Morse theory for M and prove, in particular, that M has the homotopy type of a space obtained from a manifold fibered over a circle, by attaching cells.

Circle-valued Morse theory and Reidemeister torsion Michael Hutchings Yi-Jen Lee Dept of Math, Stanford University, Stanford, CAUSA Dept of Math, Princeton Circle-Valued Morse Theory book, Princeton, NJUSA Email: [email protected] and [email protected] Abstract Let X be a closed manifold with ˜(X)=0,andletf:X!S1be a circle-valued.

CIRCLE-VALUED MORSE THEORY FOR FRAME SPUN KNOTS AND SURFACE-LINKS HISAAKI ENDO AND ANDREI PAJITNOV Nk •Sk 2 be a closed oriented submanifold, denote its comple- ment by CpNq Sk by ˘PH1pCpNqqthe class dual to Morse-Novikov number of CpNqis by deﬁnition the minimal possible number ofAuthor: Hisaaki Endo, Andrei Pajitnov.

simplest version of NovikovÕs construction, we consider a circle-valued Morse function /:XPS1. There is an analogue of the Morse complex which counts gradient ßow lines of /.

In this circle-valued case, to obtain a Þnite count we need to classify ßow lines using some information about their homotopy classes. A minimal way to do this is as. CIRCLE-VALUED MORSE THEORY FOR COMPLEX HYPERPLANE ARRANGEMENTS 5 obvious since fα(µz) = µα1 + αm f α(z) for µ ∈ R+, therefore f0 α(z) 6= 0 for every z /∈ H, since all αi are positive.

The proof of Lemma is now over. ⁄ For a subset X ⊂ Cn and δ > 0 let us denote by X(δ) the subset of all z ∈ Cn such that d(z,X) 6 δ.

Proposition Let Γ ⊂ Rm. The Morse theory of circle valued functions f: M → S1 relates the topology of a manifold M to the critical points of f, generalizing the traditional theory of real valued Morse functions M → R.

However, the relationship is somewhat more complicated in the circle valued case. circle-valued morse theory for complex hyperplane arrangements 11 IP MU, G R AD UA TE S CHOOL OF M A TH EM ATI C AL S CI E NC ES, TH E U NI VE RS IT Y OF T OK YO, 3- 8- 1 K O MA BA, M E GU RO.

Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. Novikov in the early s. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory of Lagrangian intersections, fibrations of manifolds.

Circle-valued Morse theory and Reidemeister torsion. Circle valued Morse theory is necessarily more complicated than real valued Morse theory. The Morse-Smale complex CMS(M;f: M!R;v) is an absolute object, describing M on the chain level, with c0(f) >0, cm(f) >0.

This is the algebraic analogue of the fact that every continuous function f: M!Ron a compact space attains an absolute minimum.

Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. 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.

Circle-valued Morse theory Saved in: Restrictions on access to electronic version: access available to SOAS staff and students only, using SOAS id and password. Home» MAA Publications» MAA Reviews» Circle-valued Morse Theory.

Circle-valued Morse Theory. Andrei V. Pajitnov. Publisher: Walter de Gruyter. Publication Date: Number of Pages: Format: Hardcover. Category: Monograph. MAA Review; Table of Contents; We do not plan to review this book. Morse Theory and Floer Homology (Universitext) by Michèle Audin, Mihai Damian, et al.

out of 5 stars 2 by Morse, Janice M., PhD (Nurs), PhD (Anthro), FCAHS, FAAN. Kindle Audible Listen to Books & Original Audio Performances. Circle-valued Morse Theory. Series:De Gruyter Studies in Mathematics ,95 € / $ / £* Add to Cart. Book Book Series. Frontmatter Get Access to Full Text. Contents.

Get Access to Full Text. Circle-valued Morse maps and Novikov complexes. CHAPTER Completions of rings, modules and complexes. circle-valued Mo rse function f: M!S 1 is not so w ell-understo o d. Objective: mak e the Novik ov complex as w ell-understo o d as the Mo rse-Smale com-plex!

F eed algeb ra back into top ology. The strategy: lift f: M!S 1 to in - nite cyclic covers f: M!R and compa re CNov (f) to CMSfN), with fN = fj: MN f − 1 [0; 1]!

; The general theo ry.Summary: InM 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. This book aims to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions.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.

英文书摘要 In 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.