Three Dimensional Link Theory And Invariants Of Plane Curve Singularities Am 110 Volume 110

Author : David Eisenbud
Publisher : Princeton University Press
ISBN 13 : 1400881927
Total Pages : 180 pages
Book Rating : 4.25/5 ( download)

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Download or read book Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 written by David Eisenbud and published by Princeton University Press. This book was released on 2016-03-02 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Author : David Eisenbud
Publisher : Princeton University Press
ISBN 13 : 9780691083810
Total Pages : 188 pages
Book Rating : 4.19/5 ( download)

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Download or read book Three-dimensional Link Theory and Invariants of Plane Curve Singularities written by David Eisenbud and published by Princeton University Press. This book was released on 1985 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Author : Helmut Hofer
Publisher : Springer Nature
ISBN 13 : 3031191110
Total Pages : 1158 pages
Book Rating : 4.14/5 ( download)

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Download or read book Symplectic Geometry written by Helmut Hofer and published by Springer Nature. This book was released on 2022-12-05 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author : Yukio Matsumoto
Publisher : Springer
ISBN 13 : 3642225349
Total Pages : 251 pages
Book Rating : 4.45/5 ( download)

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Download or read book Pseudo-periodic Maps and Degeneration of Riemann Surfaces written by Yukio Matsumoto and published by Springer. This book was released on 2011-08-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Author : Craig D. Hodgson
Publisher : American Mathematical Soc.
ISBN 13 : 0821884808
Total Pages : 395 pages
Book Rating : 4.05/5 ( download)

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Download or read book Geometry and Topology Down Under written by Craig D. Hodgson and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.

Author : James A. Carlson
Publisher : American Mathematical Soc.
ISBN 13 : 0821814923
Total Pages : 358 pages
Book Rating : 4.25/5 ( download)

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Download or read book Complex Geometry and Lie Theory written by James A. Carlson and published by American Mathematical Soc.. This book was released on 1991 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 1960s and early 1970s, Phillip Griffiths and his collaborators undertook a study of period mappings and variation of Hodge structure. The motivating problems, which centered on the understanding of algebraic varieties and the algebraic cycles on them, came from algebraic geometry. However, the techiques used were transcendental in nature, drawing heavily on both Lie theory and hermitian differential geometry. Promising approaches were formulated to fundamental questions in the theory of algebraic curves, moduli theory, and the deep interaction between Hodge theory and algebraic cyles. Rapid progress on many fronts was made in the 1970s and 1980s, including the discovery of important connections to other fields, including Nevanlinna theory, integrable systems, rational homotopy theory, harmonic mappings, intersection cohomology, and superstring theory. This volume contains thirteen papers presented during the Symposium on Complex Geometry and Lie Theory held in Sundance, Utah in May 1989. The symposium was designed to review twenty years of interaction between these two fields, concentrating on their links with Hodge theory. The organizers felt that the time was right to examine once again the large issues of understanding the moduli and cycle theory of higher-dimensional varieties, which was the starting point of these developments. The breadth of this collection of papers indicates the continuing growth and vitality of this area of research. Several survey papers are included, which should make the book a valuable resource for graduate students and other researchers who wish to learn about the field. With contributions from some of the field's top researchers, this volume testifies to the breadth and vitality of this area of research.

Author : Boris N. Apanasov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110784106
Total Pages : 534 pages
Book Rating : 4.07/5 ( download)

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Download or read book Dynamics of Discrete Group Action written by Boris N. Apanasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.

Author : András Némethi
Publisher : Springer
ISBN 13 : 3642236472
Total Pages : 241 pages
Book Rating : 4.71/5 ( download)

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Download or read book Milnor Fiber Boundary of a Non-isolated Surface Singularity written by András Némethi and published by Springer. This book was released on 2012-01-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Author : Anna Beliakova
Publisher : American Mathematical Soc.
ISBN 13 : 1470428210
Total Pages : 282 pages
Book Rating : 4.11/5 ( download)

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Download or read book Categorification in Geometry, Topology, and Physics written by Anna Beliakova and published by American Mathematical Soc.. This book was released on 2017-02-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Author : Boris N. Apanasov
Publisher : Walter de Gruyter
ISBN 13 : 3110805057
Total Pages : 361 pages
Book Rating : 4.55/5 ( download)

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Download or read book Geometry, Topology and Physics written by Boris N. Apanasov and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.