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   Sun, Jing; Rudnick, Roberta L.; Kostrovitsky, Sergey; Kalashnikova, Tatiana; Kitajima, Kouki; Li, Ranpeng; Shu, Qiao (March 2020, Contributions to Mineralogy and Petrology)

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   https://doi.org/10.4153/S0008439523000383  

   Amelotte, Steven; Briggs, Benjamin (December 2023, Canadian Mathematical Bulletin)

   Abstract A simple polytopePis calledB-rigidif its combinatorial type is determined by the cohomology ring of the moment-angle manifold$$\mathcal {Z}_P$$overP. We show that any tensor product decomposition of this cohomology ring is geometrically realized by a product decomposition of the moment-angle manifold up to equivariant diffeomorphism. As an application, we find thatB-rigid polytopes are closed under products, generalizing some recent results in the toric topology literature. Algebraically, our proof establishes that the Koszul homology of a Gorenstein Stanley–Reisner ring admits a nontrivial tensor product decomposition if and only if the underlying simplicial complex decomposes as a join of full subcomplexes. 

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   Luo, Yantao; Korenaga, Jun (December 2020, Geology)

   null (Ed.)

   Continental lithospheric mantle (CLM) may have been built from subducted slabs, but the apparent lack of concurrent oceanic crust in CLM, known as the mass imbalance problem, remains unresolved. Here, we present a simple dynamic model to evaluate the likelihood of losing dense eclogitized oceanic crust from CLM by gravitational instability. Our model allowed us to assess the long-term evolution of such crust removal, based on how thermal and viscosity profiles change over time across the continental lithosphere. We found that the oceanic crust incorporated early into CLM can quickly escape to the asthenosphere, whereas that incorporated after a certain age would be preserved in CLM. This study provides a plausible explanation for the mass imbalance problem posed by the oceanic ridge origin hypothesis of CLM and points to the significance of preservation bias inherent to the studies of cratonic diamonds. 

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