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A knot move illustrated above. Two knots cannot be distinguished using Vassiliev invariants of order <=n iff they are related by a sequence of such moves (Habiro 2000). There ...

A diagram expressing how the gluing operation that connects the handlebodies involved in a Heegaard splitting proceeds, usually by showing how the meridians of the handlebody ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

A disjunction that remains true if either or both of its arguments are true. This is equivalent to the OR connective. By contrast, the exclusive disjunction is true if only ...

An inner automorphism of a group G is an automorphism of the form phi(g)=h^(-1)gh, where h is a fixed element of G. The automorphism of the symmetric group S_3 that maps the ...

A negative-height (inward-pointing) pyramid used in augmentation. The term was introduced by B. Grünbaum.

The term used in propositional calculus for the NOR connective. The notation AvB is used for this connective.

A generalization of the concept of set unions and intersections.

A formula which counts the number of fixed points for a topological transformation.

A type I move (conjugation) takes AB->BA for A, B in B_n where B_n is a braid group. A type II move (stabilization) takes A->Ab_n or A->Ab_n^(-1) for A in B_n, and b_n, Ab_n, ...