A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated. Suppose we consider a generalized notion of bistellar flips that are non-topological, ie, they can duplicate existing faces of complexes. For instance, on a 3-simplex, a (2,2) non-topological flip would map one edge of the tetrahedron into the edge it does not intersect.

Is this notion already defined in the literature? Which classes of nontopological bistellar flips are known to preserve the type of a manifold? It seems likely to me that in low dimensions a good deal may already be known.

A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated. Suppose we consider a generalized notion of bistellar flips that are non-topological, i.e., they can duplicate existing faces of complexes. For instance, on a 3-simplex, a (2,2) non-topological flip would map one edge of the tetrahedron into the edge it does not intersect.

Is this notion already defined in the literature? Which classes of nontopological bistellar flips are known to preserve the type of a manifold? It seems likely to me that in low dimensions a good deal may already be known.

A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated. Suppose we consider a generalized notion of bistellar flips that are non-topological, ie, they can duplicate existing faces of complexes

Is this notion already defined in the literature? Which classes of nontopological bistellar flips are known to be manifold-preserving on particular kinds of manifolds? It seems likely to me that in low dimensions a good deal may already be known.

A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated. Suppose we consider a generalized notion of bistellar flips that are non-topological, ie, they can duplicate existing faces of complexes. For instance, on a 3-simplex, a (2,2) non-topological flip would map one edge of the tetrahedron into the edge it does not intersect.

Is this notion already defined in the literature? Which classes of nontopological bistellar flips are known to preserve the type of a manifold? It seems likely to me that in low dimensions a good deal may already be known.

A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated.

Does any full-dimensional topological bistellar flip applied to a triangulated d-sphere always result in a triangulated d-sphere? This fact seems like it may be obvious: is there a simple way to see why?

More generally, is there a good reference for results on which classes of bistellar flips are known to be manifold-preserving on particular kinds of manifolds? It seems likely to me that in low dimensions a good deal must be already known.

A topological bistellar flip is the term used by Dougherty, Faber, and Murphy to describe a bistellar flip that does not cause any face of a complex to be duplicated. Suppose we consider a generalized notion of bistellar flips that are non-topological, ie, they can duplicate existing faces of complexes

Is this notion already defined in the literature? Which classes of nontopological bistellar flips are known to be manifold-preserving on particular kinds of manifolds? It seems likely to me that in low dimensions a good deal may already be known.