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The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

The indices of a contravariant tensor A^j can be lowered, turning it into a covariant tensor A_i, by multiplication by a so-called metric tensor g_(ij), e.g., g_(ij)A^j=A_i.

The indices of a covariant tensor A_j can be raised, forming a contravariant tensor A^i, by multiplication by a so-called metric tensor g^(ij), e.g., g^(ij)A_j=A^i

A branch of topology dealing with topological invariants of manifolds.

The number of ways in which a group of n with weights sum_(i=1)^(n)w_i=1 can change a losing coalition (one with sumw_i<1/2) to a winning one, or vice versa. It was proposed ...

A theorem which states that the analytic and topological "indices" are equal for any elliptic differential operator on an n-dimensional compact smooth C^infty boundaryless ...

The index set for the collection of submodules in a graded module.

A multiple series is a series involving sums over more than one index.

Exotic cohomology is a cohomology theory that extends index theory to a larger class of manifolds.

The formal term used for a collection of objects. It is denoted {a_i}_(i in I) (but other kinds of brackets can be used as well), where I is a nonempty set called the index ...