Abstract
The Cartan formula encodes the relationship between the cup product and the action of the Steenrod algebra in Fp-cohomology. In this work, we present an effective proof of the Cartan formula at the cochain level when the field is F2. More explicitly, for an arbitrary pair of cocycles and any non-negative integer, we construct a natural coboundary that descends to the associated instance of the Cartan formula. Our construction of Cartan coboundaries works for general algebras over the Barratt-Eccles operad, in particular, for the singular cochains of spaces, a case for which we have developed open source software.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.