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The dual to a tetrahedron consists of a single vertex at which four edges andsix faces are incident. Along each edge, three faces converge. A 2-foam is acompact topological space such that each point has a neighborhood homeomorphicto a neighborhood of that complex. Knotted foams in 4-dimensional space are toknotted surfaces, as knotted trivalent graphs are to classical knots. Thediagram of a knotted foam consists of a generic projection into 4-space withcrossing information indicated via a broken surface. In this paper, a finiteset of moves to foams are presented that are analogous to the Reidemeister-typemoves for knotted graphs. These moves include the Roseman moves for knottedsurfaces. Given a pair of diagrams of isotopic knotted foams there is a finitesequence of moves taken from this set that, when applied to one diagramsequentially, produces the other diagram.

Reidemeister/Roseman-type Moves to Embedded Foams in 4-dimensional Space