Deck transformation

A deck transformation maps sheets to sheets

Let be a covering and be a Deck transformation. Let , be an evenly covered open neighbourhood of , and be a sheet over . Then is also a sheet over . homotopy

Proof

Given a deck transformation , the following diagram commutes.

Let be an evenly covered connected open set and be a sheet over . Then is connected and , so for some sheet over . Let . Then so there exists some such that . But is injective in so Therefore .

---

tidy | en | sembr