Norihiko Minami

The iterated transfer analogue of the new doomsday conjecture

A strong general restriction is given on the stable Hurewicz image of the classifying spaces of elementary abelian p-groups. In particular, this implies the iterated transfer analogue of the new doomsday conjecture.

The Kervaire invariant one element and the double transfer

Abstract The Kervaire invariant one element θj ϵ πs2j + 1 − 2(S0) is shown not to factor through the double transfer unless j ≦ 4. In particular, θ5 of Barratt-Jones-Mahowald does not factor through the double transfer.

On the odd-primary Adams 2-line elements

Abstract A couple of results on the odd-primary Adams 2-line elements are recorded here: First, the odd-primary Kervaire invariant one element θ j ∈ π s qp j +1 −2 ( S 0 ) is shown not to factor through the double transfer unless j ≤2 (respectively j =0) when p =3 (respectively p ≥5). Second, the odd-primary η j element is shown to have (a nonzero multiple of) β 1 as its James–Hopf invariant.

Nilpotency of the Bauer-Furuta stable homotopy Seiberg-Witten invariants

We prove a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants for smooth closed 4-manifolds with trivial first Betti number.

Borsuk-Ulam type theorems for compact Lie group actions

Borsuk-Ulam type theorems for arbitrary compact Lie group actions are proven. The transfer plays a major role in this approach.