Rotating sleeve is the piece that's on the CT end of a 36mm hose. Description from our website:
Replacement Rotating Hose Connector for attaching Festool Antistatic D 36 (36mm) hoses to the inlet of the CT 22, CT 26, CT 33 and CT 36 Dust Extractors. External diameter 58 mm. Use replacement rotating connectors and reducing sleeves to create new custom sized hoses from longer lengths, or use to replace damaged parts. Antistatic components are only effective when used as part of a complete antistatic dust extraction system, including extractors or vacuums, hoses, sleeves and couplings.
Edited: I accidentally said "end of a stock hose" instead of "36mm hose".
To clarify Bob's statement, the 36mm hose goes on the outside of the extraction connection on most of our tools. The 27mm goes on the inside of the connection. No adapter necessary.