Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with homology
Search options not deleted
user 168142
Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
3
votes
0
answers
130
views
Homology groups of a certain simplicial complex
I've run across a simplicial complex which, according to Sage, seems to have a very easily-described homology. However, proving this fact has been rather difficult. … Then we need to prove that the other reduced homology groups are zero, which shouldn't be as difficult. …
- 807
1
vote
Amending flawed "proof" that homology groups are zero
. ▮
We'll also use the Mayer--Vietoris sequence, which for reduced homology states that
$$\eqalign{
\cdots \to H_s(A)\oplus H_s(B) \to H_s(X)\to H_{s-1}(A\cap B) \to
H_{s-1}(A)\oplus H_{s-1}(B)\to\cr …
- 807
7
votes
4
answers
996
views
Amending flawed "proof" that homology groups are zero
In the following, when we speak of homology of $\Delta_n$ and write $H_k(\Delta_n)$, we mean homology over ${\bf Z}$.
Proposition. For all $k\ge 1$, $H_k(\Delta_n)=0$.
"Proof". … The $k$th homology of this simplicial subcomplex is zero, so the $(k+2)$-tuple $(x_1,\ldots,x_{k+2})$ contributes nothing to the $k$th
homology of $\Delta_n$. …
- 807