## A method for visualizing cohomology aspects of 3D objects

*J.M. Berrio*

`jmberrio@sadiel.es`

Applied Mathematics Dept., CS

**Seville University**

Avda. Reina Mercedes s/n

Spain

*R. Gonzalez-Diaz*

`rododi@us.es`

Applied Mathematics Dept., CS

**Seville University**

Avda. Reina Mercedes s/n

Spain

*F. Leal*

`wes_mont@teleline.es`

Applied Mathematics Dept., CS

**Seville University**

Avda. Reina Mercedes s/n

Spain

*M.M. Lopez-Maraver*

`jmberrio@sadiel.es`

Applied Mathematics Dept., CS

**Seville University**

Avda. Reina Mercedes s/n

Spain

*P. Real*

`real@cica.es`

Applied Mathematics Dept., CS

**Seville University**

Avda. Reina Mercedes s/n

Spain

### Abstract

We propose here a method for visualizing homology, algebra
cohomology, cohomology operations and cup-i products of 3D
objects.

First of all, we give simplicial-based representations
of three dimensional objects, essentially using a suitable
tetrahedral decomposition of a cube.
In order to compute the
homology and cohomology of a given object, the first step in our
method is the topological thinning of a simplicial complex which
represents this object. From the resulting skeleton, the second
step is to compute the algebraic invariants mentioned above.

From
the point of view of the implementation, the graphical user
interface of this method is presented in this paper and some
examples concerning topological thinning and computation of the
cochain operations cup-i products (see [1]) are
discussed.

[1] J.R. Munkres. Elements of Algebraic Topology, Addison-Wesley
Publishing Company, 1984.

© ATCM, Inc. 2001.