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C.F.G
C.F.G
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One can build a projective plane from R^n$\Bbb R^n$, C^n$\Bbb C^n$ and H^n$\Bbb H^n$ and is then tempted to do the same for octonions. This leads to the construction of a projective plane known as OP^2$\Bbb OP^2$, the Cayley projective plane.

What are the references for the properties of the Cayley projective plane  ? In particular, I would like to know its (co)homology and homotopy groups.

Also, what geometric intuition works when working with this object? Does the intuition from real projective space transfer well or does the non-associativity make a large difference? For example, I would like to know why one could have known that there is no OP^3$\Bbb OP^3$.

One can build a projective plane from R^n, C^n and H^n and is then tempted to do the same for octonions. This leads to the construction of a projective plane known as OP^2, the Cayley projective plane.

What are the references for the properties of the Cayley projective plane  ? In particular, I would like to know its (co)homology and homotopy groups.

Also, what geometric intuition works when working with this object? Does the intuition from real projective space transfer well or does the non-associativity make a large difference? For example, I would like to know why one could have known that there is no OP^3.

One can build a projective plane from $\Bbb R^n$, $\Bbb C^n$ and $\Bbb H^n$ and is then tempted to do the same for octonions. This leads to the construction of a projective plane known as $\Bbb OP^2$, the Cayley projective plane.

What are the references for the properties of the Cayley projective plane? In particular, I would like to know its (co)homology and homotopy groups.

Also, what geometric intuition works when working with this object? Does the intuition from real projective space transfer well or does the non-associativity make a large difference? For example, I would like to know why one could have known that there is no $\Bbb OP^3$.

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skupers
skupers
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What is the Cayley projective plane?

One can build a projective plane from R^n, C^n and H^n and is then tempted to do the same for octonions. This leads to the construction of a projective plane known as OP^2, the Cayley projective plane.

What are the references for the properties of the Cayley projective plane ? In particular, I would like to know its (co)homology and homotopy groups.

Also, what geometric intuition works when working with this object? Does the intuition from real projective space transfer well or does the non-associativity make a large difference? For example, I would like to know why one could have known that there is no OP^3.