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5 votes
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A struggle with jets and Grothendieck vs Ehresmann connections

Let $X\to Y$ be a $C^\infty$ submersion. Consider the following two sheaves. The sheaf on $Y$ comprised of jets of sections of $X\to Y$. The sheaf on $X$ given by the quotient of $\Delta_{X/Y}^{-1}C^\...
Arrow's user avatar
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3 votes
0 answers
522 views

Writing a Taylor series with covariant derivatives (connections)?

A connection of a vector bundle $E$ on a manifold $M$ is a map $d_E: \Omega^0(E) \to \Omega^1(E)$ that extends uniquely to a map $d_E: \Omega^p(E) \to \Omega^{p+1}(E)$ while satisfying $$ d_E(\omega \...
Ma Joad's user avatar
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1 vote
0 answers
90 views

Curvature of a superconnection

Let $E\rightarrow X$ be a $\mathbb{Z}_2$-vector bundle (or superbundle for connoisseurs) and consider the superconnection $$A=\nabla + B$$ where $\nabla$ is a connection on $E$ and $B\in\Gamma(End(E))^...
BinAcker's user avatar
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