Euler classIn mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characteristic. It is named after Leonhard Euler because of this. Throughout this article is an oriented, real vector bundle of rank over a base space . The Euler class is an element of the integral cohomology group constructed as follows.
Refusal of workRefusal of work is behavior in which a person refuses regular employment. As actual behavior, with or without a political or philosophical program, it has been practiced by various subcultures and individuals. It is frequently engaged in by those who critique the concept of work, and it has a long history. Radical political positions have openly advocated refusal of work. From within Marxism it has been advocated by Paul Lafargue and the Italian workerist/autonomists (e.g. Antonio Negri, Mario Tronti), the French ultra-left (e.
Working classThe working class, sometimes incorrectly referred to as the middle class, includes all employees who are compensated with wage or salary-based contracts. Working-class occupations (see also "Designation of workers by collar colour") include blue-collar jobs, and most pink-collar jobs. Members of the working class rely exclusively upon earnings from wage labour; thus, according to more inclusive definitions, the category can include almost all of the working population of industrialized economies, as well as those employed in the urban areas (cities, towns, villages) of non-industrialized economies or in the rural workforce.
Pontryagin classIn mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four. Given a real vector bundle E over M, its k-th Pontryagin class is defined as where: denotes the -th Chern class of the complexification of E, is the -cohomology group of M with integer coefficients. The rational Pontryagin class is defined to be the image of in , the -cohomology group of M with rational coefficients.
Chern classIn mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of mathematics and physics, such as string theory, Chern–Simons theory, knot theory, Gromov-Witten invariants. Chern classes were introduced by . Chern classes are characteristic classes. They are topological invariants associated with vector bundles on a smooth manifold.
Social classA social class or social stratum is a grouping of people into a set of hierarchical social categories, the most common being the upper, middle and lower classes. Membership in a social class can for example be dependent on education, wealth, occupation, income, and belonging to a particular subculture or social network. "Class" is a subject of analysis for sociologists, political scientists, anthropologists and social historians. The term has a wide range of sometimes conflicting meanings, and there is no broad consensus on a definition of "class".
