The rise of computerized trading strategies in equity markets has spurred competition between trading venues. This paper shows that cross-venue strategies create highly interlinked markets: trades on one venue are followed by sizeable cancellations of limit orders on competing venues. These cancellations are explained in a simple model of competition between two limit order markets with fast and slow traders. Only the fast traders can access the liquidity of both venues simultaneously. Empirically, we confirm the predictions that the fraction of fast traders (1) reduces the equilibrium liquidity supply and (2) reduces the magnitude of the cancellations following a trade.