3-Manifolds, tangles and persistent invariants

Jozef H. Przytycki, Daniel S. Silver, Susan G. Williams

Published 2004-05-24Version 1

New obstructions for embedding one compact oriented 3-manifold in another are given. A theorem of D. Krebes concerning 4-tangles embedded in links arises as a special case. Algebraic and skein-theoretic generalizations for 2n-tangles provide invariants that persist in the corresponding invariants of links in which they embed. An example is given of a virtual 4-tangle for which Krebes's theorem does not hold.