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