A combinatorial method for computing Steenrod squares

A Combinatorial Method for Computing Steenrod Squares

We present here a combinatorial method for computing cup-i products and Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A genera...

O ct 2 00 1 A COMBINATORIAL METHOD FOR COMPUTING STEENROD SQUARES

We present here a combinatorial method for computing cup-i products and Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A genera...

A combinatorial method for computing

We present here a combinatorial method for computing Steenrod squares of a simplicial set X . This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X . A generalization of this ...

Computation of Cubical Steenrod Squares

Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in R. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher tha...

On the omputability of Steenrod squares