arXiv subjects

Dana Hunter

Publications and source records attributed to Dana Hunter.

2 recordsLinked to original sources

arXiv2024

A prop structure on partitions

Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Yoneda product of extensions between exterior power functors.

math.AT↗

arXiv2021

The Curtis-Wellington spectral sequence through cohomology

We study stable homotopy through unstable methods applied to its representing infinite loop space, as pioneered by Curtis and Wellington. Using cohomology instead of homology, we find a width filtration whose subquotients are simple quotients of Dickson algebras. We make initial calculations and determine towers in the resulting width spectral sequence. We also make calculations related to the image of $J$ and conjecture that it is captured exactly by the lowest filtration in the width spectral sequence.

math.AT↗