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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

1 vote

Fredholm property of linearization of Floer map

They show in Section 8.7.c that $(dF^H)_u$ is a Fredholm operator. What remains is simple linear algebra (even continuity is irrelevant). Suppose $A: V \times W \to U$ is a linear map, with $B = A|_V$ …
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8 votes
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Nonvanishing section of infinite-dimensional tautological bundle

Let $X$ be any paracompact space. Then Hilbert vector bundles over $X$ are classified by homotopy classes of maps $[X, BU(\mathcal H)]$. But when $\mathcal H$ is infinite-dimensional, the group $U(\ma …
mme's user avatar
  • 9,580
2 votes
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Orientability of moduli space and determinant bundle of ASD operator

You want a line bundle that's well-defined over the entire space of irreducible connections $\mathcal B^*$; this is how you see, for instance, that a choice of orientation at one point in the moduli s …
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  • 9,580