Decompositions of Manifolds
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 331 |
| Release | : 1986-12-22 |
| Genre | : Mathematics |
| ISBN | : 0080874436 |
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Decompositions of Manifolds
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Decompositions of Manifolds
| Author | : Robert J. Daverman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 317 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9780821843727 |
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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
| Author | : R. H. Bing |
| Publisher | : |
| Total Pages | : 288 |
| Release | : 1983-07 |
| Genre | : Mathematics |
| ISBN | : |
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Cellular Decompositions of 3-Manifolds that Yield 3-Manifolds
| Author | : Steve Armentrout |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 76 |
| Release | : 1971 |
| Genre | : Decomposition (Mathematics) |
| ISBN | : 0821818074 |
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Hodge Decomposition - A Method for Solving Boundary Value Problems
| Author | : Günter Schwarz |
| Publisher | : Springer |
| Total Pages | : 161 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540494030 |
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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.
Foliations and the Geometry of 3-Manifolds
| Author | : Danny Calegari |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 378 |
| Release | : 2007-05-17 |
| Genre | : Mathematics |
| ISBN | : 0198570082 |
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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 |
| Total Pages | : 798 |
| Release | : 2021-02-10 |
| Genre | : Mathematics |
| ISBN | : 3030624978 |
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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.
Handlebody Decompositions of Complex Surfaces
| Author | : John Harer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 1986 |
| Genre | : Geometry, Algebraic |
| ISBN | : 0821823515 |
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This monograph gives framed link pictures of the Kummer surface (= [italic]V4) and some Dolgachev surfaces. The emphasis here is to use the elliptic pencil structure to describe the framed links. This approach is particularly convenient to see the change of handlebody structures of elliptic surfaces after an operation of logarithmic transform, which is an important ingredient in constructing Dolgachev surfaces.
Introduction to Knot Theory
| Author | : R. H. Crowell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 191 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461299357 |
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Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.
High-dimensional Knot Theory
| Author | : Andrew Ranicki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 669 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662120119 |
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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.
