A Combinatorial Method for Computing Steenrod Squares
arXiv:math/0110308 · doi:10.1016/S0022-4049(99)00006-7
Abstract
We present here a combinatorial method for computing cup- products and Steenrod squares of a simplicial set . 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 . A generalization of this method to Steenrod reduced powers is sketched. This description can be considered as a translation of the most ancient definition of Steenrod squares to the general setting of the Simplicial Topology.
25 pages
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- Cyclification of Orbifolds
- Steenrod coalgebras
- Computing Cocycles on Simplicial Complexes
- Steenrod operations via higher Bruhat orders
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- Computation of Cohomology Operations on Finite Simplicial Complexes