Reidemeister/Roseman-type moves to embedded foams in 4-dimensional space
JS Carter - arXiv preprint arXiv:1210.3608, 2012 - arxiv.org
arXiv preprint arXiv:1210.3608, 2012•arxiv.org
The dual to a tetrahedron consists of a single vertex at which four edges and six faces are
incident. Along each edge, three faces converge. A 2-foam is a compact topological space
such that each point has a neighborhood homeomorphic to a neighborhood of that complex.
Knotted foams in 4-dimensional space are to knotted surfaces, as knotted trivalent graphs
are to classical knots. The diagram of a knotted foam consists of a generic projection into 4-
space with crossing information indicated via a broken surface. In this paper, a finite set of …
incident. Along each edge, three faces converge. A 2-foam is a compact topological space
such that each point has a neighborhood homeomorphic to a neighborhood of that complex.
Knotted foams in 4-dimensional space are to knotted surfaces, as knotted trivalent graphs
are to classical knots. The diagram of a knotted foam consists of a generic projection into 4-
space with crossing information indicated via a broken surface. In this paper, a finite set of …
The dual to a tetrahedron consists of a single vertex at which four edges and six faces are incident. Along each edge, three faces converge. A 2-foam is a compact topological space such that each point has a neighborhood homeomorphic to a neighborhood of that complex. Knotted foams in 4-dimensional space are to knotted surfaces, as knotted trivalent graphs are to classical knots. The diagram of a knotted foam consists of a generic projection into 4-space with crossing information indicated via a broken surface. In this paper, a finite set of moves to foams are presented that are analogous to the Reidemeister-type moves for knotted graphs. These moves include the Roseman moves for knotted surfaces. Given a pair of diagrams of isotopic knotted foams there is a finite sequence of moves taken from this set that, when applied to one diagram sequentially, produces the other diagram.
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