# Higher Spinor Classes

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## Higher Spinor Classes

### Higher Spinor Classes by J. F. Jardine Book Summary:

This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Frohlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 etale cohomology.

## Higher Spinor Classes

### Higher Spinor Classes by J. F. Jardine Book Summary:

This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Frohlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 etale cohomology.

## Higher Multiplicities and Almost Free Divisors and Complete Intersections

### Higher Multiplicities and Almost Free Divisors and Complete Intersections by James Damon Book Summary:

In this book, the author considers a general class of nonisolated hypersurface and complete intersection singularities called 'almost free divisors and complete intersections', which simultaneously extend both the free divisors introduced by K. Saito and the isolated hypersurface and complete intersection singularities. They also include discriminants of mappings, bifurcation sets, and certain types of arrangements of hyperplanes, such as Coxeter arrangements and generic arrangements. Topological properties of these singularities are studied via a 'singular Milnor fibration' which has the same homotopy properties as the Milnor fibration for isolated singularities.The associated 'singular Milnor number' can be computed as the length of a determinantal module using a Bezout-type theorem. This allows one to define and compute higher multiplicities along the lines of Teissier's $\mu ^*$-constants. These are applied to deduce topological properties of singularities in a number of situations including: complements of hyperplane arrangements, various nonisolated complete intersections, nonlinear arrangements of hypersurfaces, functions on discriminants, singularities defined by compositions of functions, and bifurcation sets. It treats nonisolated and isolated singularities together. It uses the singular Milnor fibration with its simpler homotopy structure as an effective tool. It explicitly computes the singular Milnor number and higher multiplicities using a Bezout-type theorem for modules.

## The Index Theorem for Minimal Surfaces of Higher Genus

### The Index Theorem for Minimal Surfaces of Higher Genus by Friedrich Tomi,Anthony Tromba Book Summary:

The question of estimating the number of minimal surfaces that bound a prescribed contour has been open since Douglas's solution of the Plateau problem in 1931. In this book, the authors formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. The Index Theorem for Minimal Surfaces of Higher Genus describes, in terms of Fredholm Index, a rough measure on the set of curves bounding minimal surfaces of prescribed branching type and genus.

## The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras

### The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras by Hans Plesner Jakobsen Book Summary:

This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.

## On Finite Groups and Homotopy Theory

### On Finite Groups and Homotopy Theory by Ran Levi Book Summary:

Let $p$ be a fixed prime number. Let $G$ denote a finite $p$-perfect group. This book looks at the homotopy type of the $p$-completed classifying space $BG_p$, where $G$ is a finite $p$-perfect group. The author constructs an algebraic analog of the Quillen's plus'' construction for differential graded coalgebras. This construction is used to show that given a finite $p$-perfect group $G$, the loop spaces $BG_p$ admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general $B\ast _p$ admits infinitely many non-trivial $k$-invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.

## Forthcoming Books

### Forthcoming Books by Rose Arny Book Summary:

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## Notices of the American Mathematical Society

### Notices of the American Mathematical Society by American Mathematical Society Book Summary:

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## Reviews in Number Theory, 1984-96

### Reviews in Number Theory, 1984-96 by N.A Book Summary:

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

## Journal de théorie des nombres de Bordeaux

### Journal de théorie des nombres de Bordeaux by N.A Book Summary:

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## Mathematical Reviews

### Mathematical Reviews by N.A Book Summary:

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## The Cumulative Book Index

### The Cumulative Book Index by N.A Book Summary:

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## Memoirs of the American Mathematical Society

### Memoirs of the American Mathematical Society by N.A Book Summary:

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## Internationale mathematische Nachrichten

### Internationale mathematische Nachrichten by N.A Book Summary:

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

## Clifford Algebras and Spinor Structures

### Clifford Algebras and Spinor Structures by Rafal Ablamowicz,P. Lounesto Book Summary:

This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.

## Clifford Algebras and Spinors

### Clifford Algebras and Spinors by Pertti Lounesto Book Summary:

This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.

## Introduction to Physics of Elementary Particles

### Introduction to Physics of Elementary Particles by O. M. Boyarkin Book Summary:

In this textbook, all known fundamental interactions are considered and the main directions of their unification are reviewed. The basic theoretical ideas and experiments, which permit establishing a quark-lepton level of matter structure are discussed. A general scheme for the theory of interacting fields with the help of the local gauge invariance principle is given. This scheme is used for presentation of the basic aspects of the quantum chromodynamics and electroweak theory of Weinberg-Salam-Glashow. Principles of operation and designs of accelerators, neutrino telescopes, and elementary particle detectors are considered. The modern theory of the Universe evolution is described.