Surgery obstructions and character varieties

Abstract

We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in $S^3$. In contrast with previously known examples, our proofs do not require any gauge theory or Floer homology. Instead, we make use of the $SU(2)$ character variety of the fundamental group, which for these manifolds is particularly simple: they are all $SU(2)$-cyclic, meaning that every $SU(2)$ representation has cyclic image.

32 pages, 4 figures; v2: accepted version

References in corpus (2)

• SU(2)-cyclic surgeries and the pillowcase
• A menagerie of SU(2)-cyclic 3-manifolds