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Two manifolds are said to be diffeomorphic if there exists a diffeomorphism between them.

A set of points which do not lie on any of a certain class of hyperplanes.

Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

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

The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A Liouville Space, also known as line space or "extended" Hilbert space, it is the Cartesian product of two Hilbert spaces.