Deck transformation

A deck transformation¹ of a covering $𝑝 : ˜ 𝑋 ↠ 𝑋$ is an automorphism of $𝑝$ in $𝖢 𝗈 𝗏 𝑋$ .² #m/def/homotopy The set of all deck transformations $A u t 𝖢 𝗈 𝗏 𝑋 (𝑝)$ is clearly a subgroup of the group of homeomorphisms of $˜ 𝑋$ , called the deck transformation group³. The deck transformation group has a natural group action on the covering space $˜ 𝑋$ by application.