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

Effects of organism preparation in metallothionein and metal analysis in marine invertebrates for biomonitoring marine pollution

Metallothionein (MT) is established as a potentially useful biomarker for monitoring aquatic pollution. This paper addresses widespread inconsistencies in storage conditions, tissue type selection and pre-treatment of samples before MT and metal analysis in biomarker studies. This variation hampers comparability and so the widespread implementation of this monitoring approach. Actively sampled Mytilus edulis in Southampton Water, UK were exposed to different storage temperatures, a variety tissue types were analysed, and various pre-treatments of transportation on ice, transportation in seawater, depuration, and rapid dissection in the field were examined. Storage temperatures of -20?C were found to be adequate for periods of at least ten weeks, as MT was not reduced by protein degradation compared with samples kept at -80?C. Whole tissue and digestive gland concentrations of MT and metals were significantly positively correlated and directly relatable. MT in the digestive gland appeared to be more responsive to metals than in whole tissue, where it may be diluted, masking MT responses. However, longer study periods may suffer the effects of mass changes to the digestive gland, which alters MT concentration, and it may therefore be advisable to measure whole tissue. Depuration and transportation in seawater reduced both MT and metal concentrations in the digestive gland, and few correlations between MT and metals were identified for these treatments. It is therefore recommended that: i) samples are transported to the laboratory on ice and dissected as soon as possible thereafter, ii) depuration should not be used when examining MT response to metal exposure until further research clarifying its utility is reported, iii) either whole tissue or the digestive gland can be used to measure MT, though whole tissue may be preferable on long-term studies, and iv) organisms can be stored at -20?C before analysis for up to ten weeks. These practices can be applied to future biomonitoring studies and will improve the comparability and repeatability of using MT as a biomarker

Metal accumulation and metallothionein response in Fucus spiralis

Seaweeds are established sentinels for metal contamination and are utilised for biomonitoring. Metallothionein (MT) is a protein that is induced by metal exposure, and has been widely used as a biomarker for metal pollution. MT has not been reported in spiral wrack (Fucus spiralis), but has been identified in bladder wrack (Fucus vesiculosus), where it has been suggested as a protective mechanism against metal exposure. This study aimed to evaluate the potential use of MT in F. spiralis as a biomarker for metal pollution for the first time. Samples were collected from Poole Harbour, UK, over a year-long period, from January to October 2015. MT and metal concentrations were quantified during winter, spring, summer, and autumn seasons. Linear regression analysis showed few relationships between MT and metal concentrations, apart from in summer. During summer, significant positive relationships existed between MT concentrations and iron (R2 = 0.631), nickel (R2 = 0.486), tin (R2 = 0.579), and lead (R2 = 0.415). It is possible that for most of the year, metal concentrations in Poole Harbour are not high enough to elicit a MT response in F. spiralis, as it is a metal tolerant species. However, during summer, rates of photosynthesis and growth increase, which may increase metal toxicity, due to the inhibition of photosynthesis and growth. Thus, MT may be induced in order to prevent disruption. This study suggests that the use of MT as a biomarker for metal pollution in F. spiralis may not be a sensitive biomarker at low levels of metal pollution. However, MT concentrations in F. spiralis may respond to metal exposure when natural processes are vulnerable to pollution. The potential for MT to be used as a biomarker in Fucus spp. has been highlighted, warranting further research to develop a promising cosmopolitan bioindicator for metal pollution