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In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable forms which cannot be continuously ...

Regge calculus is a finite element method utilized in numerical relativity in attempts of describing spacetimes with few or no symmetries by way of producing numerical ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

A real vector bundle pi:E->M has an orientation if there exists a covering by trivializations U_i×R^k such that the transition functions are vector space ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

Topology

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.