It is our working hypothesis that the high rate of the liver and gastric cancers in North and Northeast Thailand is associated with increased daily dietary intake of nitrate, nitrite, and nitrosodimethylamine (NDMA). Samples of fresh and preserved Thai foods were systematically collected and analyzed from 1988 to 1996 and from 1998 to 2005. Consumption frequencies of various food items were determined on the basis of a dietary questionnaire given to 467 adults (212 males and 255 females) from 1998 to 2005. Food consumption data for the preceding and current year were collected and intakes (day, week, and month) of nitrate, nitrite, and NDMA were calculated. The trends in liver and stomach cancer age-standardized incidence rates (ASR) in four regions of Thailand were compared with the dietary intake of nitrate, nitrite, and NDMA in those same geographic regions. Mean daily intakes of nitrate of 155.7 mg/kg, of nitrite of 7.1 mg/kg, and of NDMA of 1.08 microg/kg per day were found. Significant differences in dietary nitrate, nitrite, and NDMA intakes were seen between various Thai regions (P < 0.0001), and these corresponded to the variations in liver and stomach cancer ASR values between the regions. Dietary factors are likely to play key roles in different stages of liver and stomach carcinogenesis in Thailand.
We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for Stiefel-Whitney numbers of (finite covers of) the Gromov-Thurston examples of negatively curved manifolds. We mention some geometric corollaries: the MinVol question, a lower bound for degrees of covers having tangential maps to the non-negatively curved duals, and estimates for the complexity of some representations of certain uniform lattices.
Abstract. We are concerned with the implications of the Freiheitssatz property for certain group presentations in terms of proper homotopy invariants of the underlying group, by describing its fundamental pro-group. A finitely presented group G is said to be properly 3-realizable if it is the fundamental group of a finite 2-dimensional CW-complex whose universal cover has the proper homotopy type of a 3-manifold. We show that if an infinite finitely presented group G is given by some special kind of presentation satisfying the Freiheitssatz, then G is semistable at infinity and properly 3-realizable. In particular, this applies to groups given by a staggered presentation.
In this paper, we consider an equivalence relation within the class of finitely presented discrete groups attending to their asymptotic topology rather than their asymptotic geometry. More precisely, we say that two finitely presented groups G and H are "proper 2-equivalent" if there exist (equivalently, for all) finite 2-dimensional CW-complexes X and Y , with π 1 (X) ∼ = G and π 1 (Y ) ∼ = H, so that their universal covers X and Y are proper 2-equivalent. It follows that this relation is coarser than the quasi-isometry relation. We point out that finitely presented groups which are 1-ended and semistable at infinity are classified, up to proper 2-equivalence, by their fundamental progroup, and we study the behaviour of this relation with respect to some of the main constructions in combinatorial group theory. A (finer) similar equivalence relation may also be considered for groups of type Fn, n ≥ 3, which captures more of the large-scale topology of the group. Finally, we pay special attention to the class of those groups G which admit a finite 2-dimensional CW-complex X with π 1 (X) ∼ = G and whose universal cover X has the proper homotopy type of a 3-manifold. We show that if such a group G is 1-ended and semistable at infinity then it is proper 2-equivalent to either Z × Z × Z, Z × Z or F 2 × Z (here, F 2 is the free group on two generators). As it turns out, this applies in particular to any group G fitting as the middle term of a short exact sequence of infinite finitely presented groups, thus classifying such group extensions up to proper 2-equivalence.Date: December 1, 2019.
In this paper, we show that the direct product of infinite finitely presented groups is always properly 3-realisable. We also show that classical hyperbolic groups are properly 3-realisable. We recall that a finitely presented group G is said to be properly 3-realisable if there exists a compact 2-polyhedron K with TTI(K) = G and whose universal cover K has the proper homotopy type of a (p.l.) 3-manifold with boundary. The question whether or not every finitely presented is properly 3-realisable remains open.
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