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 …

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. …

A genus-2 surface. In mathematics, genus (pl.: genera) has a few different, but closely related, meanings. Intuitively, the genus is the number of "holes" of a surface. [1] A sphere has genus …

A genus $2$ surface can be constructed by starting with a wedge sum of $4$ circles $\{a_1, b_1, a_2, b_2\}$ and attaching a $2$-cell along $[a_1, b_1] [a_2, b_2]$. The fundamental group is …

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 …

2019年3月25日 · First homology group of a double torus is H1(T2#T2) =Z4, H 1 (T 2 # T 2) = Z 4, (where # stands for a connected sum) which – for me – intuitively means there are 4 different …

2020年12月8日 · So using Vam-kampen, I obtained the fundamental group for the genus two surface to be $$\langle a,b,c,d|aba^{-1}b^{-1}(cdc^{-1}d^{-1})^{-1}\rangle = \langle …

2012年3月23日 · 我是想用粘对边的方法来把两个torus粘起来。 genus 2的torus先割成两个genus 1的torus，并且留下一条边界，然后每个torus割成一个正方形，但是怎么在这个正方形里 …

6 天之前 · A sphere with two handles and two holes, i.e., a genus-2 torus.

1992年10月1日 · Riemann's second bilinear relation follows: the imaginary part of the period matrix {7cij} is positive definite. The Siegel space Tg is the space of all symmetric g x g …