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YCor
YCor
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a principle bundle is a good fibration, with moral fiber
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Allen Knutson
Allen Knutson
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Given a topological space $M$ with a locally free $S^1$ action on it, assume the slice representation holds,(this is often the case, e.g. M is a smooth manifold) then this will make $M$ a principleprincipal $S^1$-orbibundle over $M/S^1$. What's the proper way to define the Euler class of this $S^1$-orbibundle? How should the naturality of Euler class be stated in the category of $S^1$-orbibundles?

Given a topological space $M$ with a locally free $S^1$ action on it, assume the slice representation holds,(this is often the case, e.g. M is a smooth manifold) then this will make $M$ a principle $S^1$-orbibundle over $M/S^1$. What's the proper way to define the Euler class of this $S^1$-orbibundle? How should the naturality of Euler class be stated in the category of $S^1$-orbibundles?

Given a topological space $M$ with a locally free $S^1$ action on it, assume the slice representation holds,(this is often the case, e.g. M is a smooth manifold) then this will make $M$ a principal $S^1$-orbibundle over $M/S^1$. What's the proper way to define the Euler class of this $S^1$-orbibundle? How should the naturality of Euler class be stated in the category of $S^1$-orbibundles?

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Shisen Luo
Shisen Luo
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Euler class of S^1-orbibundle

Given a topological space $M$ with a locally free $S^1$ action on it, assume the slice representation holds,(this is often the case, e.g. M is a smooth manifold) then this will make $M$ a principle $S^1$-orbibundle over $M/S^1$. What's the proper way to define the Euler class of this $S^1$-orbibundle? How should the naturality of Euler class be stated in the category of $S^1$-orbibundles?