9 problems

Geometric Gamma-operation generation conjecture. $\Omega^{S^1}$ is generated over geometric versions of the operations $\Gamma_V$ by linear actions on projective spaces.

Projective-space generation conjecture. Stably complex $S^1$ actions with isolated fixed points up to bordism are generated by linear actions on projective spaces

Pull-back conjecture. The square

Kosniowski's conjecture. If $M^{2n}$ is not a boundary, then the number of fixed points is greater than $f(n)$. Kosniowski conjectured that the candidate function is

Let $T^k$ be the $k$-torus and let $\mathbb{Z}_2^k$ be its real subgroup. Write $\Omega^{U,T^k}_{2*}$ and $\Omega^{U,\mathbb{Z}_2^k}_{2*}$ for the unitary equivariant bordism group…

Guillemin–Ginzburg–Karshon's conjecture. An element $\beta\in\Omega_*^{U,G}$ is zero if and only if all integral equivariant cohomology Chern numbers of $\beta$ vanish.

Let $M^{2n}$ be a nonbounding unitary toric manifold, meaning that it does not bound equivariantly, and let $\lceil n/2\rceil$ denote the least integer greater than or equal to…

Let $\mathcal{Z}_{2n}^{U}(T^n)$ be the group of $T^n$-equivariant unitary bordism classes of $2n$-dimensional unitary toric manifolds, let $\mathcal{Q}_*$ be the graded noncommutat…

Let $M$ be a connected closed manifold, let $f\colon M\to M$ be a self-map, and let $n\geq 2$. For the homotopy $n$-periodic point space, let $\ell_n^k(f)$ denote the relevant comp…