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…
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…
Making the motivic group structure on the endomorphisms of the projective line explicit
Viktor Balch Barth, William Hornslien, Gereon Quick +1
We construct a group structure on the set of pointed naive homotopy classes of scheme morphisms from the Jouanolou device to the projective line. The group operation is defined via…
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…