arXiv subjects
Publications and source records attributed to William Ghanem.
We prove that rational homology ribbon cobordism defines a partial order on the set of homeomorphism classes of closed, connected, oriented 3-manifolds. More precisely, if $W_0 \leq W_1$ and $W_1 \leq W_0$, then $W_0$ and $W_1$ are homeomorphic by an orientation preserving homeomorphism.
We introduce boundary quotients and present a framework for learning densities on manifolds that arise as boundary quotients of simpler domains. We show that this framework can be used to construct normalizing flows on quotient manifolds $N/G$, where a discrete group $G$ acts on $N$. We instantiate this construction for genus-$g$ surfaces $\Sigma_g$. When $G$ is finite, we show applicability to symmetry aware learning; we demonstrate this on cyclic quotients of the 3-sphere. Experiments on lens spaces show that simple pre-quotient RealNVP models can achieve strong results while being substantially cheaper to evaluate.