# Tag Info

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### How to make associated ribbon surface?

First, on your hand drawn graph, you have the red arrows reversed in one segment on the right side. After you fix that the glueing works as follows. Close off each ribbon with a small line segment. ...
• 5,258
1 vote
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### If a submanifold is homeomorphic to the ambient manifold but is a proper subset, then the inclusion map can't be proper

Your argument looks correct to me. Note that depending on the definition of submanifolds, you may need to add the assumption that $N$ does not have boundary. In fact an inclusion with locally compact ...
• 7,762
1 vote

### What is the Geometric Interpretation of the Addition of n-Singular Simplices?

You did not miss anything: there's no particular geometric intuition, it's really just algebraic formalities. A chain is just a "vector" assigning a numerical coordinate to each singular ...
• 109k
1 vote

### What is the connection between the two definitions of homology in 1.1 of Rotman's An Introduction to Homological Algebra?

Don't worry, Rotman just wants to give examples of the use of the term "homology" in mathematics. It should be a motivational introduction, but I am afraid that it is not really a felicitous ...
• 67.2k
1 vote

### Is there a symmetric embedding of the torus in $\mathbb{R}^3$?

If the embedding is locally the standard embedding of the $2$-disk in the $3$-disk then we can define orientations using local homology and follow ideas from the comments to the question. Since $s$ ...
• 7,762
1 vote

### Existence of a cone neighbourhood in an open disc with a point in the border

If the authors meant anything else by "cone neighborhood" than a neighborhood of $a$ that is also a cone, they surely would have given a definition for the phrase. You will have to check ...
• 40.6k
1 vote

### Existence of a cone neighbourhood in an open disc with a point in the border

By cone neighbourhood in P do they mean a cone $aL$ such that $aL\subset P$ is true and also there is an open subset $O\subset P$ such that $a\in O\subset aL$? Yes, a cone neighborhood of $a \in P$ ...
• 67.2k
1 vote

### Understanding why collapsing $CX$ and $CY$ gives us $\sum (X \times Y)$?

This is an extra-long proof of $1$. My hope is that after reading it thoroughly several times, you'll be equipped to answer question 2 and 3 yourself. The definition of the (reduced) join \$(X,x_0)\...
• 48.8k

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