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An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...

Let U=(U,<··>) be a T2 associative inner product space over the field C of complex numbers with completion H, and assume that U comes with an antilinear involution xi|->xi^* ...

A strong pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, the map v_m|->g_m(v_m,·) is an ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

The cyclotomic graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a cube in the finite field GF(q). This graph is ...

A codimension one foliation F of a 3-manifold M is said to be taut if for every leaf lambda in the leaf space L of F, there is a circle gamma_lambda transverse to F (i.e., a ...