3 - Manifolds , Tangles and Persistent Invariants
نویسنده
چکیده
Given a compact, connected, oriented 3-manifold M with boundary, and epimorphism χ from H1M to a free abelian group Π, two invariants β, τ ∈ ZΠ are defined. If M embeds in another such 3manifold N such that χN factors through χ, then the product βτ divides ∆0(H1Ñ). 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.
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