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A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

A Brunnian link is a set of n linked loops such that each proper sublink is trivial, so that the removal of any component leaves a set of trivial unlinked unknots. The ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

A compact manifold without boundary.

Let p be a non-wandering point of a diffeomorphism S:M->M of a compact manifold. The closing lemma concerns if S can be arbitrarily well approximated with derivatives of ...

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...