I am taking a first course in topology, and I am struggling with simplicial complexes. Specifically the triangulation of subspaces of $ \mathbb{R}^n $ confuses me. If you could help me on the following points I would be very grateful. In general how do you construct a triangulation of a subspace? I have been given […]

I refer to example 4, fig.3.6, p.17 of Munkres’ Algebraic Topology. He says the given triangulation scheme “does more than paste opposite edges together”. Not clear to me. For those who don’t have the book to hand, a rectangle is divided into 6 equal squares by a horizontal midline and two verticals; each square has […]

I was asked to find out the simplicial homology groups of the torus $T=S^1\times{}S^1$ embedded in $R^3$. I triangulated the torus like this : Here the $0$-simplices are $\{v_0\}$. $1$-simplices are $\{a,b,c\}$ and the $2$-simplices are $\{D_1,D_2\}$. And I found out the homology groups : $H_0(T)=\mathbb{Z}, H_1(T)=\mathbb{Z}^2,H_2(T)=\mathbb{Z}$ But my teacher said it was wrong, because […]

I am writing a program and I need to calculate the 3rd point of a triangle if the other two points, all sides and angles are known. A (6,14) ^ / \ 14.14 / \ 10.14 / \ / \ B (16,4)——— C (x,y) 10.98 A (6,14), B (16,4). Side AB is 14.14, AC is […]

How many ways are there to triangulate a regular convex n-gon, if two triangulations are regarded as being the same if they can be made to coincide by a rotation of the polygon? I found that for a hexagon that there are 14 triangulations but there are triangulations that are just rotations of the others. […]

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