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Author: Christine Lescop Publisher: Princeton University Press ISBN: 1400865158 Category : Mathematics Languages : en Pages : 156
Book Description
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Author: Christine Lescop Publisher: Princeton University Press ISBN: 1400865158 Category : Mathematics Languages : en Pages : 156
Book Description
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Author: Christine Lescop Publisher: Princeton University Press ISBN: 0691021325 Category : Mathematics Languages : en Pages : 155
Book Description
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Author: András Némethi Publisher: Springer Nature ISBN: 3031067533 Category : Mathematics Languages : en Pages : 732
Book Description
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.
Author: Ga.) Georgia International Topology Conference (2001 : Athens Publisher: American Mathematical Soc. ISBN: 0821835076 Category : Differential topology Languages : en Pages : 370
Book Description
Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.
Author: Oliver Sacks Publisher: Vintage ISBN: 0345805887 Category : Psychology Languages : en Pages : 336
Book Description
To these seven narratives of neurological disorder Dr. Sacks brings the same humanity, poetic observation, and infectious sense of wonder that are apparent in his bestsellers Awakenings and The Man Who Mistook His Wife for a Hat. These men, women, and one extraordinary child emerge as brilliantly adaptive personalities, whose conditions have not so much debilitated them as ushered them into another reality.
Author: Takeyoshi Dohi Publisher: Springer Science & Business Media ISBN: 3540442251 Category : Computers Languages : en Pages : 722
Book Description
The fifth international Conference in Medical Image Computing and Computer Assisted Intervention (MICCAI 2002) was held in Tokyo from September 25th to 28th, 2002. This was the first time that the conference was held in Asia since its foundation in 1998. The objective of the conference is to offer clinicians and scientists the opportunity to collaboratively create and explore the new medical field. Specifically, MICCAI offers a forum for the discussion of the state of art in computer-assisted interentions, medical robotics, and image processing among experts from multi-disciplinary professions, including but not limited to clinical doctors, computer scientists, and mechanical and biomedical engineers. The expectations of society are very high; the advancement of medicine will depend on computer and device technology in coming decades, as they did in the last decades. We received 321 manuscripts, of which 41 were chosen for oral presentation and 143 for poster presentation. Each paper has been included in these proceedings in eight-page full paper format, without any differentiation between oral and poster papers. Adherence to this full paper format, along with the increased number of manuscripts, surpassing all our expectations, has led us to issue two proceedings volumes for the first time in MICCAI’s history. Keeping to a single volume by assigning fewer pages to each paper was certainly an option for us considering our budget constraints. However, we decided to increase the volume to offer authors maximum opportunity to argue the state of art in their work and to initiate constructive discussions among the MICCAI audience.
Author: Christine Lescop
Author: Christine Lescop
Author: Christine Lescop
Author: C. Lescop
Author: András Némethi
Author: Sylvain Cappell
Author: Ga.) Georgia International Topology Conference (2001 : Athens
Author: 
Author: 
Author: Oliver Sacks
Author: Takeyoshi Dohi