Remove the tough, outer part and stalk of the fennel. Slice the bulb as finely as you can across the grain. Keep any of the green tops.
Heat 2 tablespoons oil in a thick-bottomed pan, add the garlic, fennel seeds, and chilis and cook to soften. Add the crab, zest and lemon juice, and season. Stir through, just to heat up the crab.
Cook the linguine in boiling salted water for 5 minutes, then add the fennel slices, and cook together until al dente. Drain the pasta, keeping a little of the water, and add to the crab mixture. Stir thoroughly to combine, adding a little of the reserved water to loosen the sauce, if necessary.