17 problems

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

Greenlees's conjecture. This map is an isomorphism for all abelian compact Lie groups $A$.

Let $n$ be a positive integer. The group $\mathcal{Z}_n((\mathbb{Z}_2)^n)$ is the group of $n$-dimensional equivariant unoriented bordism classes for the action of…

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…

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

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…

Let $M$ satisfy the assumptions of Theorem or Theorem; namely, in the first case, $M$ is a connected, oriented, closed manifold of even dimension with a semi-free $S^1$-action whos…

Let $G$) be a finite group, and let $\Omega^{U,G}_*$ denote the unitary $G$-equivariant bordism groups of a point, regarded as modules over the unitary bordism ring $\Omega^U_*$. F…

Let $G$ be a finite group, and let $\Omega_*^G$ denote the equivariant unitary bordism groups, regarded as modules over the unitary bordism ring $\Omega_*$. Evenness conjecture. Th…

Let $p$ be a prime, let $n$ be a positive integer, and let Theorem 1 of the source denote the paper's main theorem concerning the Brown–Peterson homology of $\wedge^n \mathbb{Z}/p$…

Conner–Floyd conjecture. The annihilator ideal of this element in $\operatorname{BP}_*$ is

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 $\mathcal{Z}_{2n}^{U}(T^n)$ 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…

Let $M$ be a closed manifold, let $f\colon M\to M$ be a self-map, and let $n\geq 2$. Let $\ell_n(f)\in\Omega_0^{\mathbb Z_n,\operatorname{fr}}(\operatorname{ho}P_n(f))$ be the homo…