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Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The ith Stiefel-Whitney class of a real vector bundle (or tangent bundle or a real manifold) is in the ith cohomology group of the base space involved. It is an obstruction ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

An optical illusion named after British psychologist James Fraser, who first studied the illusion in 1908 (Fraser 1908). The illusion is also known as the false spiral, or by ...

An optical illusion consisting of a spinnable top marked in black with the pattern shown above. When the wheel is spun (especially slowly), the black broken lines appear as ...

A two-dimensional generalization of the Haar transform which is used for the compression of astronomical images. The algorithm consists of dividing the 2^N×2^N image into ...

An optical illusion due to the physiologist Ewald Hering in 1861. The two horizontal lines are both straight, but they look as if they were bowed outwards. The distortion is ...