# Ancient/folklore

## Fundamental group torsion for subsets of Euclidean 3-space ★★

Author(s): Ancient/folklore

\begin{problem} Does there exist a subset of $\mathbb R^3$ such that its fundamental group has an element of finite order? % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. \end{problem}

Keywords: subsets of euclidean space; torsion

## Which homology 3-spheres bound homology 4-balls? ★★★★

Author(s): Ancient/folklore

\begin{problem} Is there a complete and computable set of invariants that can determine which (rational) homology $3$-spheres bound (rational) homology $4$-balls? % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. \end{problem}

Keywords: cobordism; homology ball; homology sphere

## Odd perfect numbers ★★★

Author(s): Ancient/folklore

\begin{conjecture} There is no odd \Def{perfect number}. \end{conjecture}

Keywords: perfect number