590 B
590 B
Whoa very cool
In this series of quests we will prove that the fundamental group
of S¹ is ℤ.
In fact, our strategy will also show that the higher homotopy groups of
S¹ are all trivial.
We begin by formalising the problem statement.
The Circle
A contruction of 'the circle' is :
- a point
- an edge from that point to itself
Here is our definition of the circle in agda.
data S¹ : Type where
base : S¹
loop : base ≡ base
The base \== base is the space of paths from base to base.
An "edge" is the same as a path.