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A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n-k)-forms. If w is an ...

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type (1,0). In a coordinate chart z=(z_1,...,z_n), the bundle ...

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

The prime link 02-0201 which has Jones polynomial V(t)=-t-t^(-1) and HOMFLY polynomial P(z,alpha)=z^(-1)(alpha^(-1)-alpha^(-3))+zalpha^(-1). It has braid word sigma_1^2.

A 4-hyperboloid has negative curvature, with R^2=x^2+y^2+z^2-w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)-2w=0. (2) Since r=xx^^+yy^^+zz^^, (3) it follows that ...

A continuum that is not decomposable is an indecomposable continuum.

Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the ...

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.