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Pontryagin-Chern number

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  • Chern class — In mathematics, in particular in algebraic topology and differential geometry, the Chern classes are characteristic classes associated to complex vector bundles. Chern classes were introduced by Shiing Shen Chern (1946). Contents 1 Basic… …   Wikipedia

  • Pontryagin class — In mathematics, the Pontryagin classes are certain characteristic classes. The Pontryagin class lies in cohomology groups with index a multiple of four. It applies to real vector bundles. Definition Given a vector bundle E over M , its k th… …   Wikipedia

  • Characteristic class — In mathematics, a characteristic class is a way of associating to each principal bundle on a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is twisted particularly, whether it possesses… …   Wikipedia

  • Generalized Gauss–Bonnet theorem — In mathematics, the generalized Gauss–Bonnet theorem (also called Chern–Gauss–Bonnet theorem) presents the Euler characteristic of a closed even dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It …   Wikipedia

  • List of algebraic topology topics — This is a list of algebraic topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of geometric topology topics Publications in topology Topological property Contents 1… …   Wikipedia

  • André Weil — Infobox Scientist name = André Weil image width = caption = birth date = birth date|1906|5|6 birth place = Nantes death date = death date and age|1998|8|6|1906|5|6 death place = field = Mathematics work institutions = Lehigh University… …   Wikipedia

  • Curvature invariant (general relativity) — Curvature invariants in general relativity are a set of scalars called curvature invariants that arise in general relativity. They are formed from the Riemann, Weyl and Ricci tensors which represent curvature and possibly operations on them such… …   Wikipedia

  • Instanton — An instanton or pseudoparticle is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang Mills instanton is a self dual or anti self dual connection in a principal bundle over a four dimensional Riemannian manifold… …   Wikipedia

  • Generalized Gauss-Bonnet theorem — In mathematics, the generalized Gauss Bonnet theorem presents the Euler characteristic of a closed even dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It is a direct generalization of the Gauss… …   Wikipedia

  • Minimal volume — In mathematics, in particular in differential geometry, the minimal volume is a number that describes one aspect of a Riemannian manifold s topology. This invariant was introduced by Mikhail Gromov. Contents 1 Definition 2 Related topological… …   Wikipedia

  • Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia

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