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Free, publicly-accessible full text available February 1, 2025
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Abstract Let $M$ be a closed, odd GKM$_3$ manifold of non-negative sectional curvature. We show that in this situation one can associate an ordinary abstract GKM$_3$ graph to $M$ and prove that if this graph is orientable, then both the equivariant and the ordinary rational cohomology of $M$ split off the cohomology of an odd-dimensional sphere.more » « less
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Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n -manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we showthe Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.more » « less
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Liu, Kefeng (Ed.)We endow each closed, orientable Alexandrov space (X, d) with an integral current T of weight equal to 1, ∂T = 0 and set(T) = X, in other words, we prove that (X, d, T) is an integral current space with no boundary. Combining this result with a result of Li and Perales, we show that non-collapsing sequences of these spaces with uniform lower curvature and diameter bounds admit subsequences whose Gromov-Hausdorff and intrinsic flat limits agree.more » « less
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null (Ed.)Abstract Freshwater pollution is a major global concern. Common methods for determining the effects of contaminants on freshwater organisms involve short-term laboratory experiments with otherwise healthy organisms. However, in natural systems, organisms are commonly exposed to parasites, which could alter their ability to survive exposure to aquatic contamination. We used a freshwater crustacean (Daphnia dentifera) to quantify the effects of parasite exposure on mortality from two common freshwater contaminants (elevated salinity [NaCl] and carbaryl). In our salinity trial, both parasite exposure and elevated salinity reduced survival in an additive manner. In our carbaryl trial, exposure to carbaryl reduced survival and we found a less-than-additive (i.e. antagonistic) interaction between carbaryl and the parasite; the parasite only reduced survival in the control (no carbaryl) treatments. Our results demonstrate that parasites and contaminants can jointly affect mortality in aquatic organisms in an additive or less-than-additive manner.more » « less
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Wei, Guofang (Ed.)We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry.more » « less