orientable surface
21Haken manifold — In mathematics, a Haken manifold is a compact, P² irreducible 3 manifold that contains a two sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable,… …
22Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …
23Klein bottle — In mathematics, the Klein bottle is a certain non orientable surface, i.e. , a surface (a two dimensional manifold) with no distinct inner and outer sides. Other related non orientable objects include the Möbius strip and the real projective… …
24Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
25Lickorish–Wallace theorem — In mathematics, the Lickorish–Wallace theorem in the theory of 3 manifolds states that any closed, orientable, connected 3 manifold may be obtained by performing Dehn surgery on a framed link in the 3 sphere with +/ 1 surgery coefficients.… …
26Classification of manifolds — In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Contents 1 Main themes 1.1 Overview 1.2 Different categories and additional… …
27Graph embedding — In topological graph theory, an embedding of a graph G on a surface Sigma; is a representation of G on Sigma; in which points of Sigma; are associated to vertices and simple arcs (homeomorphic images of [0,1] ) are associated to edges in such a… …
28Y-homeomorphism — In mathematics, the y homeomorphism, or crosscap slide, is a special type of auto homeomorphism in non orientable surfaces. It can be constructed by sliding a Möbius band included on the surface around an essential 1 sided closed curve until the… …
29Trigenus — In low dimensional topology, the trigenus is an invariant consisting of a triplet:(g 1,g 2,g 3) assigned to closed 3 manifolds. The definition is by minimizing the genera of three orientable handle bodies mdash; with no intersection between their …
30Heawood conjecture — The Heawood conjecture or Ringel–Youngs theorem in graph theory gives an upper bound for the number of colors which are sufficient for graph coloring on a surface of a given genus. It was proven in 1968 by Gerhard Ringel and J. W. T. Youngs. One… …
