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15
46
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Confusion regarding definition of integrability of $G$-structure

Published on
#algebraic-topology #principal-bundles #classifying-spaces
95
Views

Showing vanishing 2nd Stiefel-Whitney class implies existence of spin structure

Published on
#algebraic-topology #principal-bundles #spin-geometry #classifying-spaces
345
Views

Can every covering space be obtained from a principal $G$-bundle with $G$ discrete?

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#algebraic-topology #covering-spaces #principal-bundles
131
Views

Confusion about the proof of $D\phi=d\phi+\rho_*(\omega)\cdot\phi$ and $D\omega=d\omega+\frac12[\omega\wedge\omega]$ in principal bundle

Published on
#differential-geometry #connections #principal-bundles #exterior-derivative
240
Views

Curvature on an Associated Vector Bundle

Published on
#differential-geometry #differential-topology #curvature #principal-bundles #gauge-theory
190
Views

Why the "horizontal" in exterior covariant derivative

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#differential-geometry #vector-bundles #principal-bundles #gauge-theory #exterior-derivative
53
Views

Associated fibre bundle to a $(\Gamma,\alpha)$-equivariant $G$-principal bundle

Published on
#reference-request #fiber-bundles #principal-bundles #topological-k-theory #equivariant-topology
100
Views

Classification of principal G-bundles

Published on
#algebraic-topology #homotopy-theory #principal-bundles #representable-functor
153
Views

Understanding the quotient (pre)stack

Published on
#category-theory #principal-bundles #algebraic-stacks
89
Views

Transformation of holonomy group under gauge transformation

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#principal-bundles #gauge-theory #holonomy
33
Views

Does every (compact?) Lie group $G$ have a representation inducing an equivalence between $G$-bundles and certain vector bundles?

Published on
#vector-bundles #principal-bundles
56
Views

Principal $PU(\mathcal H)$-bundle from a principal $\mathbb Z$-bundle and a principal $S^1$-bundle.

Published on
#homology-cohomology #principal-bundles #classifying-spaces #eilenberg-maclane-spaces
165
Views

Doubt on connection notions for the tangent bundle $T\mathcal{M}$

Published on
#differential-geometry #smooth-manifolds #vector-bundles #connections #principal-bundles
370
Views

The Lie bracket of two horizontal vector fields is vertical?

Published on
#differential-geometry #curvature #connections #principal-bundles
145
Views

Extending a principal connection form to an associated principal bundle

Published on
#differential-geometry #lie-groups #principal-bundles

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