Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

Glacial changes in sea level modulated millennial-scale variability of Southeast Asian autumn monsoon rainfall.

Most paleoclimate studies of Mainland Southeast Asia hydroclimate focus on the summer monsoon, with few studies investigating rainfall in other seasons. Here, we present a multiproxy stalagmite record (45,000 to 4,000 years) from central Vietnam, a region that receives most of its annual rainfall in autumn (September-November). We find evidence of a prolonged dry period spanning the last glacial maximum that is punctuated by an abrupt shift to wetter conditions during the deglaciation at ~14 ka. Paired with climate model simulations, we show that sea-level change drives autumn monsoon rainfall variability on glacial-orbital timescales. Consistent with the dry signal in the stalagmite record, climate model simulations reveal that lower glacial sea level exposes land in the Gulf of Tonkin and along the South China Shelf, reducing convection and moisture delivery to central Vietnam. When sea level rises and these landmasses flood at ~14 ka, moisture delivery to central Vietnam increases, causing an abrupt shift from dry to wet conditions. On millennial timescales, we find signatures of well-known Heinrich Stadials (HS) (dry conditions) and Dansgaard-Oeschger Events (wet conditions). Model simulations show that during the dry HS, changes in sea surface temperature related to meltwater forcing cause the formation of an anomalous anticyclone in the Western Pacific, which advects dry air across central Vietnam, decreasing autumn rainfall. Notably, sea level modulates the magnitude of millennial-scale dry and wet phases by muting dry events and enhancing wet events during periods of low sea level, highlighting the importance of this mechanism to autumn monsoon variability