All Questions
3 questions with no upvoted or accepted answers
5
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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^\...
3
votes
0
answers
522
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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
$$
d_E(\omega \...
1
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0
answers
90
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Curvature of a superconnection
Let $E\rightarrow X$ be a $\mathbb{Z}_2$-vector bundle (or superbundle for connoisseurs) and consider the superconnection
$$A=\nabla + B$$
where $\nabla$ is a connection on $E$ and $B\in\Gamma(End(E))^...