There might not exist a single global market, but whenever the Bitcoin price is different in these markets, there's an arbitrage opportunity. As a silly example

There might not exist a single global market, but whenever the Bitcoin price is different in these markets, there's an arbitrage opportunity. As a silly example, if the Bitcoin price was 4.000 USD in one market and 40.000 USD in another market, you could buy one Bitcoin in the first one, sell it in the second one, and pocket the 36.000 USD difference. Buying Bitcoin in a market increases the price there (suppose there were 10 Bitcoin for 4.000 USD each and 12 Bitcoin for 4.200 USD each, after the first 10 Bitcoin are bought the price is now 4.200 USD), and selling Bitcoin in a market decreases the price there (it's the same dynamic in the opposite direction). After some time, the prices will converge. That is: as long as arbitrage between the markets is viable (for instance, it must be possible to move Bitcoin and fiat between the markets at a low enough cost), even though there's no single global market, the prices will tend to be close enough.