Prev: The incomprehensible work of a precocious mathematician
Next: Elastic Numbers as a Model for DNS Expansion
From: Bacle on 7 Apr 2010 20:36
> This is a question from "Ask an Algebraic
> Topologist"
>
> Hi, everyone:
>
> I am trying to find the homology of the following
> simplicial complex K:
>
> A tetrahedral surface (i.e. a simplicial sphere) that
> intersects
>
> 2 simple triangular curves (i.e., simplicial circles)
> in a common vertex v , i.e., Let T be the tetrahedron
> and T1,T2 be the triangles,
>
> and let /\ be intersection. then:
>
> T/\T1={v}= T/\T2 .
>
> **Problem **is that I don't know if I should treat
> this as (the surface of ) a three-simplex , with
> T1,T2 just 2-subsimplices of the surface,
>
> or if I should decompose it otherwise.
>
> Thanks.
Correction: this is a 2-complex, not a 3-complex.
and all its subsimplices.

I am having trouble calculating the 2nd homology
group, because I don't know how to calculate
the incidence numbers; more specifically, the
differential of a 2-chain:

I have oriented the 3-simplex <vov1v2v3v4>

How do I find the incidence number of the

3-simplex on the 2-simplices.?.

Usually, given a 2-simplex <vov1v2>, and an incident

1-simplex , say ,<vov1>, we test if

<v2vov1> is an even or odd permutation of <vov1v2>.


*BUT* . How do we find the incidence number for

the 2-simplex <vov1v2v3v4> with respect to its

1-subsimplices, say for <vov1>.?. Do we just

check if <v2v3v4vov1> is an even/odd permutation

of <vov1v2v3v4>.?

Thanks.
 | 
Pages: 1
Prev: The incomprehensible work of a precocious mathematician
Next: Elastic Numbers as a Model for DNS Expansion