You always need an extractor hood to remove the grease and smell of cooking. you can avoid having a hood but it will discolor the walls and units faster.

there are induction hobs with a hood built in but are rare

other wise you have a hob and a hood attached to the wall or ceiling.

Have you really researched induction cooking it is not for everyone. Yes you still need an exhaust system IMO as mentioned for steam , grease and smell reduction. I have a separate induction burner I use for sauces but still prefer cooking on gas . 2 of my clients that went with induction are not all that happy with it so just mentioning the research.

I have induction (love it), but you definitely need a vent.

I have an induction cooktop w/ a downdraft behind it. Don't use the downdraft much, but of course it depends on what and how you're cooking. We don't cook meats and rarely fry, so doing a stir-fry is really the only time I feel the need to turn the vent on. And absolutely love cooking with induction, by the way.

Thank you everyone for the excellent comments - we will not go without a vent! I saw a lot of different info out there while asking and researching. I used to live in Europe and had a induction unit there, and loved it. But there is a steep learning curve when using it! There were a few burned meals before I figured out how to control it. My old one had a vent hood above, but our ceiling is vaulted and really high, too high for a vent hood. So, our designer will need to help us find a carbon vent unit we can use! Thank you!!