A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of spheres. Let N be a closed connected orientable 3-manifold. Our main result is the following description of the set Emb^6(N) of embeddings N\to R^6 up to isotopy. The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where d(u) is the divisibility of the projection of u to the free part of H_1(N;Z). The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on Emb^6(N) by embedded connected sum. It was proved that the orbit space of this action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's smoothing theory). The new part of our classification result is determination of the orbits of the action. E. g. for N=RP^3 the action is free, while for N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that for each knot l:S^3\to R^6 the embedding f#l is isotopic to f. Our proof uses new approaches involving the Kreck modified surgery theory or the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in Math. Zei

Developing Health-Based Pre-Planning Clearance Goals for Airport Remediation Following a Chemical Terrorist Attack: Decision Criteria for Multipathway Exposure Routes

In the event of a chemical terrorist attack on a transportation hub, post-event remediation and restoration activities necessary to attain unrestricted facility re-use and re-entry could require hours to multiple days. While timeframes are dependent on numerous variables, a primary controlling factor is the level of pre-planning and decision-making completed prior to chemical release. What follows is the second of a two-part analysis identifying key considerations, critical information and decision criteria to facilitate post-attack and post-decontamination consequence management activities. Decision criteria analysis presented here provides first-time, open-literature documentation of multi-pathway, health-based remediation exposure guidelines for selected toxic industrial compounds, chemical warfare agents, and agent degradation products for pre-planning application in anticipation of a chemical terrorist attack. Guideline values are provided for inhalation and direct ocular vapor exposure routes as well as percutaneous vapor, surface contact, and ingestion. Target populations include various employees as well as transit passengers. This work has been performed as a national case study conducted in partnership with the Los Angeles International Airport and The Bradley International Terminal. All recommended guidelines have been selected for consistency with airport scenario release parameters of a one-time, short-duration, finite airborne release from a single source followed by compound-specific decontamination