Singularities And Low Dimensional Topology
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Singularities And Their Interaction With Geometry And Low Dimensional Topology
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Author : Javier Fernández de Bobadilla
language : en
Publisher: Springer Nature
Release Date : 2021-05-27
Singularities And Their Interaction With Geometry And Low Dimensional Topology written by Javier Fernández de Bobadilla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-27 with Mathematics categories.
The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.
Singularities And Low Dimensional Topology
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Author : Andras Stipsicz
language : en
Publisher: Springer
Release Date : 2024-06-24
Singularities And Low Dimensional Topology written by Andras Stipsicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-24 with Mathematics categories.
The special semester 'Singularities and low dimensional topology' in the Spring of 2023 at the Erdős Center (Budapest) brought together algebraic geometers and topologists to discuss and explore the strong connection between surface singularities and topological properties of three- and four-dimensional manifolds. The semester featured a Winter School (with four lecture series) and several focused weeks. This volume contains the notes of the lecture series of the Winter School and some of the lecture notes from the focused weeks. Topics covered in this collection range from algebraic geometry of complex curves, lattice homology of curve and surface singularities to novel results in smooth four-dimensional topology and grid homology, and to Seiberg-Witten homotopy theory and ‘spacification’ of knot invariants. Some of these topics are already well-documented in the literature, and the lectures aim to provide a new perspective and fresh connections. Other topics are rather new and have been covered only in research papers. We hope that this volume will be useful not only for advanced graduate students and early-stage researchers, but also for the more experienced geometers and topologists who want to be informed about the latest developments in the field.
Normal Surface Singularities
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Author : András Némethi
language : en
Publisher: Springer Nature
Release Date : 2022-10-07
Normal Surface Singularities written by András Némethi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Mathematics categories.
This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.
Deformations Of Surface Singularities
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Author : Andras Némethi
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-24
Deformations Of Surface Singularities written by Andras Némethi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-24 with Mathematics categories.
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several open problems. Recently several connections were established with low dimensional topology, symplectic geometry and theory of Stein fillings. This created an intense mathematical activity with spectacular bridges between the two areas. The theory of deformation of singularities is the key object in these connections.
Low Dimensional Topology
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Author : Samuel J. Lomonaco
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Low Dimensional Topology written by Samuel J. Lomonaco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This volume arose from a special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.
New Ideas In Low Dimensional Topology
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Author : Vassily Olegovich Manturov
language : en
Publisher: World Scientific
Release Date : 2015-01-27
New Ideas In Low Dimensional Topology written by Vassily Olegovich Manturov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-27 with Mathematics categories.
This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.
Low Dimensional Topology
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Author : Brown/Thickstun
language : en
Publisher:
Release Date : 1982
Low Dimensional Topology written by Brown/Thickstun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Topological spaces categories.
Intelligence Of Low Dimensional Topology 2006
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Author : J. Scott Carter
language : en
Publisher: World Scientific
Release Date : 2007
Intelligence Of Low Dimensional Topology 2006 written by J. Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Braid Foliations In Low Dimensional Topology
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Author : Douglas J. LaFountain
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-10-20
Braid Foliations In Low Dimensional Topology written by Douglas J. LaFountain and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Braid theory categories.
On The Topology Of Isolated Singularities In Analytic Spaces
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Author : José Seade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
On The Topology Of Isolated Singularities In Analytic Spaces written by José Seade and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-21 with Mathematics categories.
Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.