Invariant theory
Invariant theory In mathematics, invariant theory refers to the study of invariant algebraic ... if we are going to speak of invariants: that's because a scalar multiple of ... is then to define the subalgebra of invariants I(V) for the (projective) action. We ... occurrence of one-dimensional representations. The representation theory required came later, though, with Issai ...
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Knot theory
Knot theory Trefoil knot, the simplest non-trivial knot. Knot theory is a branch of topology inspired by ... depend exclusively on experiments with twine. Knot theory concerns itself with abstract properties of theoretical ... knot with its ends spliced. The topological theory of knots investigates such questions as whether ... best a minor role in the mathematical theory. A knot can be untied in ...
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Knot theory   (translated from German)
Knot theory Those Knot theory a forschungsgebiet is that Topology . It is ... the three-dimensional area. In the knot theory a knot becomes by its Projection on ... lies. Methods A goal of the knot theory is it, KnotInvariant one to find, thus ... area constantly distorts. Some examples of knot invariants are polynomials, z.B. the Jones ...
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Group theory
Group theory Group theory is that branch of mathematics concerned with ... Please refer to the Glossary of group theory for the definitions of terms used throughout group theory. See also list of group theory topics. History There are three historical ...
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Nielsen theory
Nielsen theory Nielsen theory is a branch of mathematical research with its origins in topological fixed point theory. Its central ideas were developed by Danish ... Jakob Nielsen, and bear his name. The theory developed in the study of the so ... after Nielsen's initial work, the two invariants were combined into a single "generalized ...
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Intersection theory
Intersection theory In mathematics, intersection theory is a branch of algebraic geometry, where ... are computed within the cohomology ring. The theory for varieties is older, with roots in ... Bézout's theorem on curves and elimination theory. On the other hand the topological theory more quickly reached a definitive form. ...
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Gauge theory
Gauge theory To meet Wikipedia's quality standards, this ... space-time point—they have global symmetries. Gauge theory extends this idea by requiring that the ... weak force and the strong force. This theory, known as the Standard Model, accurately describes ... forces of nature, and is a gauge theory with the gauge group SU(3) � ... � U(1). Modern theories like string theory, as well as some formulations of ...
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Percolation theory
Percolation theory In mathematics, percolation theory describes the behavior of connected clusters in ... a random graph. The applications of percolation theory to materials science and other domains is ... at and above $p\_c$ are invariants of the local structure, and therefore, in ... The critical phase Arguments from quantum field theory and quantum gravitation make a sequence ...
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Chern-Simons theory
Chern-Simons theory Chern-Simons theory is a topological gauge theory in three dimensions which describes knot and three-manifold invariants. It was introduced by Edward Witten in ... terms of a three dimensional Yang-Mills theory. It is named so because its ...
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Topological quantum field theory
Topological quantum field theory A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Overview In a topological field theory, ...
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