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Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing. The non-orientable genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n cross-caps (i.e. a non-orientable surface of (non-orientable) genus n). (This number is also called the demigenus.)
A cobordism (W; M, N).In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the property that they are constructed from a sequence of polynomials in characteristic classes that ...
In the theory of surfaces there is a more general family of objects, the "genus" g surfaces. A genus g surface is the connected sum of g two-tori. (And so the torus itself is the surface of genus 1.) To form a connected sum of two surfaces, remove from each the interior of a disk and "glue" the surfaces together along the boundary circles.
1.3 Curves with genus greater than one. 1.4 Curve families with variable genus. ... 25 Geometry and other areas of mathematics. 26 Glyphs and symbols. 27 Table of all ...
For example, the genus of a smooth projective curve C which is an interesting invariant of the curve, is an integer, which can be read off the dimension of the first Betti cohomology group of C. So, the motive of the curve should contain the genus information.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Bolza surface (genus 2) Klein quartic (genus 3) Bring's curve (genus 4)
In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.
A one-edge cut is called a bridge, isthmus, or cut edge. edge set The set of edges of a given graph G, sometimes denoted by E(G). edgeless graph The edgeless graph or totally disconnected graph on a given set of vertices is the graph that has no edges. It is sometimes called the empty graph, but this term can also refer to a graph with no vertices.