17 problems

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…

Morimoto's conjecture. The group $G$ is isomorphic to one of

Throughout, let $p$ be a prime, let $C_p={\bold Z}/p{\bold Z}$ with generator $\alpha$, and let $R={\bold Z}C_p$. For an $R$-module $M$, let $\pi_M:{\bold Z}M\to M$ be the canonica…

For an odd prime $p\geq 7$, let $X(p)$ be the modular curve of genus … with its $PSL(2,p)$-action of signature $(0;2,3,p)$. An invariant characteristic is the unique characteristic…

Let $p\geqslant 2$ be a prime number and let $(S,N)$ be a $\mathbb{Z}_p^m$-action of signature $(0;p^{n+1})$, where $2\leqslant m\leqslant n-1$. For each subgroup $L\leqslant N$ wi…

Let $X$ be a rationally connected variety of dimension $3$, and let $G\subset \mathrm{Bir}(X)$ be a finite abelian group. By the third type, we mean the case in which $G$ faithfull…

Spherical orbit-space conjecture. The space $N(P,\lambda)$ is homeomorphic to $S^n$ if and only if

Let $V_n=(\mathbb{Z}/2)^n$ and let $X$ be a finite $V_n$-CW-complex whose equivariant cohomology $H_{V_n}^*X$ is a free $H^*V_n$-module of rank $1$. Write $\operatorname{Sing}$ for…

Let $X$ be the weighted hypersurface constructed in the source, and let $G$ be the specified cyclic subgroup acting freely in codimension one on $X$, of order $m$. Since $X$ is Cal…

Let $G$ be an Oliver group and let $N$ be a normal subgroup such that … is a monomorphism. A finite group is an Oliver group if it satisfies the Oliver condition, and a Smith exoti…

Let $M$ be a closed orientable $4$-manifold with Euler characteristic $(M) \neq 0$, and let $G$ be a finite group acting effectively, locally linearly, and homologically trivially…

Almost linear k-invariant conjecture. The group $G$ acts freely and homologically trivially on a rational homology $3$-sphere with almost linear $k$-invariant if and only if $G$ ac…

Let $G$ be a finite group acting orientation-reversingly on $S^4$. Orientation-reversing linearity conjecture. $G$ is isomorphic to a subgroup of $\mathrm{O}(5)$. This is the orien…

Let $G$ be a finite group acting smoothly or locally linearly and orientation-preservingly on $S^4$. Orientation-preserving linearity conjecture. $G$ is isomorphic to a subgroup of…

Hereditary embedding conjecture. There exists a nonzero hereditary subalgebra $D\subset A$ and an injective homomorphism

Let $X$ be a free $\mathbb Z/p$-space, where $p$ is prime, and let $k$ be an integer. Suppose that $X$ is connected and acyclic over $\mathbb F_p$ in dimensions less than…

Let $M$ be a hyperbolic orientable closed $3$--manifold. A cyclic group is generated by a hyperelliptic diffeomorphism with connected nonempty fixed point set if it is generated by…