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YCor
YCor
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"can be written" is ambiguous, wrote "homeomorphic"
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YCor
YCor
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I’m interested in the question for which $n$ the special orthogonal group can be written as ais homeomorphic to the product

$$ \mathrm{SO}(n) \approx S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

I’m interested in the question for which $n$ the special orthogonal group can be written as a product

$$ \mathrm{SO}(n) \approx S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

I’m interested in the question for which $n$ the special orthogonal group is homeomorphic to the product

$$ \mathrm{SO}(n) \approx S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

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Denis Serre
Denis Serre
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I’m interested in the question for which $n$ the special orthogonal group can be written as a product

$$ \mathrm{SO}(n) = S^{n-1} \times \mathrm{SO}(n-1). $$$$ \mathrm{SO}(n) \approx S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

I’m interested in the question for which $n$ the special orthogonal group can be written as a product

$$ \mathrm{SO}(n) = S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

I’m interested in the question for which $n$ the special orthogonal group can be written as a product

$$ \mathrm{SO}(n) \approx S^{n-1} \times \mathrm{SO}(n-1). $$

Allen Hatcher [1, p. 293 f.] claims (?) that this is true for $n \in \{ 2, 4, 8 \}$ and wrong for all other values (although I’m not sure what is meant by “twisted product”).

Does anyone have a reference where this is done in more detail? Maybe I just didn’t have the right keywords for a proper search.

[1] Algebraic Topology, downloadable at https://www.math.cornell.edu/~hatcher/AT/ATpage.html

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Florian Oppermann
Florian Oppermann
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