Saw these hollow bolts in the stock air cleaner. What is the purpose of these and where does the air the goes in them go? Thanks!

 

They are the head breather bolts. Air does not go into them, but they are vent tubes that connect to a rubber hose, that is connected to the back side of the air filter. The mist that comes from the cylinder heads is burned off in the combustion chamber.

 

If I could expand on Tynker's excellent answer for a moment, all piston motors have blow-by, meaning some combustion gases go past the rings and into the crankcase instead of out the exhaust port. If the crankcase was sealed up, the crankcase pressure would build up and cause gaskets to blow out. So it has to be vented. On your motor, that venting is through those two bolts.

So what's coming out of them is essentially exhaust that went past the rings instead of out the exhaust. On it's journey through the motor, it picks up oil and water from condensation. So it's pretty nasty stuff. The EPA requires manufacturer to run this back through the engine. That's why those vents come into the air cleaner.

Since the blow by is hot and displaces oxygen and is carrying oil and water with it, running it through the motor is not desirable and it has some bad side effects. It's a very common mod to route those to the atmosphere instead, and it has some benefit - both marginally improving performance and reducing carbon build-up in the motor. Some people route them out through a little breather filter to absorb the moisture component. Others send it into a vented catch can first, that they periodically drain.

 

Don't seal those off!

 

They vent the crankcase gases back into the air intake.

If you look into replacing your air cleaner with something different, you will notice that some will allow you to vent to atmosphere and some will recirculate those gases.

Some benefits of venting to atmosphere are slightly lower intake air temperatures and you will not be sucking dirty crankcase gases into the combustion chamber.