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Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110
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.
Singularity Theory
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Singularities in Geometry, Topology, Foliations and Dynamics
This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.
Real and Complex Singularities
This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.
Singularities, Part 1
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.
Generic Bifurcations for Involutory Area Preserving Maps
This memoir describes the generic bifurcations from symmetric fixed points of families of involutory area preserving maps defined in the plane.
A Simple Definition of the Feynman Integral, with Applications
This memoir presents a simple sequential definition of the Feynman integral which is applicable to a rather large class of functionals.
On $K_*(Z/n)$ and $K_*(\mathbf {F}_q[t]/(t^2))$
This collection of papers is unified by the theme of the calculation of the low dimensional K-groups of the integers mod n and the dual numbers over a finite field.
$R$-Linear Endomorphism of $(R)_n$ Preserving Invariants
Let [italic]R be a commutative ring and ([italic]R)[subscript italic]n denote the [italic]n x [italic]n matrix ring over [italic]R. In this paper we classify the [italic]R-linear mappings [italic]T : ([italic]R)[subscript italic]n [right arrow] ([italic]R)[subscript italic]n which preserve rank one matrices. This classification gives as a corollary those [italic]R linear mappings which preserve the dominant. Other invariant preserving maps are also determined. These maps are invertible and we describe the groups that they generate.
Special Values of Dirichlet Series, Monodromy, and the Periods of Automorphic Forms
In this paper we explore a relationship that exists between the classical cusp form for subgroups of finite index in [italic]SL2([double-struck capital]Z) and certain differential equations, and we develop a connection between the equation's monodromy representation and the special values in the critical strip of the Dirichlet series associated to the cusp form.
