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Let $\mathcal{B}(X ; G)$ be the set of isomorphism classes of bundles of groups $E \rightarrow X$ with fiber $G,$ and let $E_{0} \rightarrow B$ Aut $(G)$ be the bundle corresponding to the 'identity' action $\rho: \operatorname{Aut}(G) \rightarrow \operatorname{Aut}(G) .$ Show that the map $[X, B \operatorname{Aut}(G)] \rightarrow \mathcal{B}(X, G),[f] \mapsto f^{*}\left(E_{0}\right),$ isa bijection if $X$ is a CW complex, where $[X, Y]$ denotes the set of homotopy classesof maps $X \rightarrow Y$

Calculus 3

Chapter 3

Cohomology

Section 11

Local Coefficients

Vectors

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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