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A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.
A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...
The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) ...
A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...
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.
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