In [arXiv:1602.03709v2], it was proved that Cuntz splicing a graph gives rise to a graph whose C∗-algebra is stably isomorphic to the C∗-algebra of the original graph (generalizing a result in [MR2270572]). This is used for instance in the proofs of…

In [MR1907894], Boyle proved several factorization theorems for square matrices. These theorems are the key components to go from \operatorname{SL}_{\mathcal{P}}-equivalence to flow equivalence. In this section, we prove similar factorization theore…

In the previous section, we proved that the core Kakimizu complex MS(C) is quasi-isometric to a finitely generated abelian group. To prove our main result, it remains to show that for any knot K, MS(K) is quasi-isometric to MS(C).

We have made the observation that the optimization of large portfolios minimizes the empirical risk in a regime where the data set size is similar to the size of the portfolio. In that regime, a small empirical risk does not necessarily guarantee a …