4 papers
Exotic Hopf maps, weight shifting and applications to vector bundles
Jean Fasel, William Hornslien
Using motivic homotopy theory we produce several explicit polynomial representatives of the suspension of the Hopf map defined over the integers. We derive from this computation an…
There is no Cazanave's Theorem for punctured affine space
Thomas Brazelton, William Hornslien
In his thesis, Cazanave proved that the set of naive -homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is gen…
Polyhedral products in abstract and motivic homotopy theory
William Hornslien
We introduce polyhedral products in an -categorical setting. We generalize a splitting result by Bahri, Bendersky, Cohen, and Gitler that determines the stable homotopy typ…
Polyhedral coproducts
Steven Amelotte, William Hornslien, Lewis Stanton
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We be…