Steam, crack and remove the crabmeat from the shell, making sure that little pieces of the shell are removed. Set aside.
In a wok style pan, large enough to finish off the linguine, add the olive oil. Crush and add the garlic to the pan, on a low flame lightly brown the garlic
Bring a small pot of water to boil, make an X in the bottom of the tomatoes, drop the tomatoes into the boiling water for less than a minute, enough time to loosen the skin, remove the tomatoes from the water
When the tomatoes are cool enough to handle, peel and seed the tomatoes, cut away the white core and chop the meat of the tomato into 1/4" cubes.
Chop the rosemary leaves into very small pieces
Add the chopped tomatoes to the garlic oil, on a medium low heat, cook the tomatoes with the garlic until they break down and the liquid from the tomatoes reduces, add the chopped rosemary salt and pepper to taste.
Add the cleaned crabmeat to the tomatoes, continue cooking on low heat for a few minutes, add the heavy cream. Take off the heat until the linguine has 3-4 minutes cooking time left then return it to a medium low heat.
Bring a large pot of water to boil, when the water boils, add salt, then linguine, time the cooking for 1 minute less than package indicates for al dente.
With a pasta fork, lift and drain the linguine from it's cooking water. Add to the sauce, stirring as you add, on a lively flame. After all the pasta is added, add the parmesan cheese, continue stirring. If the sauce seems too thick, thin with the pasta water