The Mayans used the corbeled vault, which is much more primitive than the arch. There's a reason people who invented arches never went back to the corbeled vault.

Compare any of the Mayan buildings with the Roman Coliseum in sophistication. I've been through Chichen Itza and spent some time looking closely at the construction of it and the neighboring buildings. I encourage you to do the same.

The Roman "style" of aqueducts used arches so they could cross valleys while maintaining a constant slope. I don't think the Mayans had that, and the Mayan aqueducts didn't seem to be very long, like 200 feet vs the Roman miles long ones.

The Romans also had hypocausts, which were a method of piping in heated air under the floor to warm the house.

The Medieval Iberia still used similar conducts to heat the cities and villages. It's impressive how much of the Roman empire (from the street layouts to home architecture) into the cities.