WebIn mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation.It is of fundamental importance for the study of 3-manifolds via their … The genus of a connected orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. It is equal to the number of handles on it. Alternatively, it can be defined in terms of the Euler characteristic … See more In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g many tori: the interior of a disk is removed from each of g many tori and the boundaries of the g … See more A genus one orientable surface is the ordinary torus. A non-orientable surface of genus one is the projective plane. Elliptic curves over the complex numbers can be identified with genus 1 surfaces. The formulation of elliptic curves as the embedding of a See more • Three-torus • g-torus knot See more • James R. Munkres, Topology, Second Edition, Prentice-Hall, 2000, ISBN 0-13-181629-2. • William S. Massey, Algebraic Topology: An … See more An orientable surface of genus zero is the sphere S . Another surface of genus zero is the disc. • Representations of genus 0 surfaces • A sphere See more The term double torus is occasionally used to denote a genus 2 surface. A non-orientable surface of genus two is the Klein bottle See more The term triple torus is also occasionally used to denote a genus 3 surface. The Klein quartic is a compact Riemann surface of genus 3 with the highest possible order See more
Genus of a surface - Encyclopedia of Mathematics
WebThis surface has equation $$ 4\sqrt{2}(x^2-y^2)z = (r^2-1)((r^2+1)^2-6z^2) $$ where $r=(x^2+y^2+z^2)^{1/2}$. It has genus two. We can build a surface like this by pasting … Web8 rows · Jul 22, 2011 · Description of value for genus surface Description of value for genus two surface ; Betti numbers: The Betti number is the rank of the torsion-free part … ez79a3lj2g-b
The genus two free boson in Arakelov geometry - ScienceDirect
Webg + 1 pairs of pipes, and one gets a g-holed surface, i.e., a surface of genus g, and a natural map (2.3) ’: M ¡! S2; which is two-to-one except for the 2g + 2 points pj = ’¡1(ej). … WebGenus definition, the usual major subdivision of a family or subfamily in the classification of organisms, usually consisting of more than one species. See more. WebMar 24, 2024 · The genus of a surface, also called the geometric genus, is related to the Euler characteristic. For a orientable surface such as a sphere (genus 0) or torus (genus … he thong dau thau dien tu bo ke hoach dau tu