Decompositions of Manifolds
Author:
Publisher: Academic Press
Published: 1986-12-22
Total Pages: 316
ISBN-13: 9780080874432
DOWNLOAD EBOOK →Decompositions of Manifolds
Lanterna Rally
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Decompositions of Manifolds
Author: Robert J. Daverman
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 317
ISBN-13: 9780821843727
DOWNLOAD EBOOK →Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to everyone who is interested in this subject. The book also contains an extensive bibliography and a useful index of key words, so it can also serve as a reference to a specialist.
Continua, Decompositions, Manifolds
Cellular Decompositions of 3-Manifolds that Yield 3-Manifolds
Author: Steve Armentrout
Publisher: American Mathematical Soc.
Published: 1971
Total Pages: 76
ISBN-13: 0821818074
DOWNLOAD EBOOK →Foliations and the Geometry of 3-Manifolds
Author: Danny Calegari
Publisher: Oxford University Press on Demand
Published: 2007-05-17
Total Pages: 378
ISBN-13: 0198570082
DOWNLOAD EBOOK →This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
2019-20 MATRIX Annals
Author: Jan de Gier
Publisher: Springer Nature
Published: 2021-02-10
Total Pages: 798
ISBN-13: 3030624978
DOWNLOAD EBOOK →MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Hodge Decomposition - A Method for Solving Boundary Value Problems
Author: Günter Schwarz
Publisher: Springer
Published: 2006-11-14
Total Pages: 161
ISBN-13: 3540494030
DOWNLOAD EBOOK →Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.
High-dimensional Knot Theory
Author: Andrew Ranicki
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 669
ISBN-13: 3662120119
DOWNLOAD EBOOK →Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
An Introduction to Contact Topology
Author: Hansjörg Geiges
Publisher: Cambridge University Press
Published: 2008-03-13
Total Pages: 8
ISBN-13: 1139467956
DOWNLOAD EBOOK →This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
Author: Gerd Grubb
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 338
ISBN-13: 082183536X
DOWNLOAD EBOOK →In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
