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 distinct tori: the interior of a disk is removed from each of g distinct …

The genus of a 3-dimensional handlebody is an integer representing the maximum number of cuttings along embedded disks without rendering the resultant manifold disconnected. It is …

I want to calculate the fundamental group of a genus-2 surface, i.e. a double torus. Using Van-Kampen I obtain ( with the notation generators- relations) $$\Pi_1(X,p) = < \alpha, \beta, …

In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. …

2019年3月25日 · First homology group of a double torus is $H_1(T^2\#T^2)=\mathbb Z^4,$ (where # stands for a connected sum) which – for me – intuitively means there are 4 different …

Figure 2. The torus T2 The torus. The torus is familiar to us as the surface of a bagel or a donut, as shown in Figure 2(a). We may describe a torus as a subspace of R3 geometrically. For …

2020年12月8日 · You should not call this surface a "2-torus", the latter means S1 ×S1 S 1 × S 1. The right name is "genus 2 surface." Fundamental groups of surfaces are usually called …

2024年5月5日 · Surfaces without boundary include a sphere and torus. The genus of a surface without boundary is the number of holes on a surface without boundary. Surfaces with …

There are two main types of surfaces: surfaces without boundary and surfaces with boundary. An invariant that can be produced from surfaces is the genus. The rigorous definition of a genus is …

2013年5月25日 · For the torus (genus 1 1) you just have the quotient of R2 R 2 by the action of Z2 Z 2 (acting by translations). The quotient is just that of a square, and it is the torus. A slight …