The Chess conjecture

We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure Math., 40 (1983) 221-224] and [VI Arnol'd, VA Vasil'ev, VV Goryunov, OV Lyashenko, Dynamical systems VI. Singularities, local and global theory, Encyclopedia of Mathematical Sciences - Vol. 6 (Springer, Berlin, 1993)]. Also, in view of the Saeki-Sakuma theorem [O Saeki, K Sakuma, Maps with only Morin singularities and the Hopf invariant one problem, Math. Proc. Camb. Phil. Soc. 124 (1998) 501-511] on the Hopf invariant one problem and Morin mappings, this implies that a manifold P^p with odd Euler characteristic does not admit Morin mappings into R^{2k+1} for p > 2k not equal to 1,3 or 7.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-26.abs.htm

Topological interpretation of color exchange invariants: hexagonal lattice on a torus

We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.Comment: 21 pages, 8 figures, Submission to SciPos

Paleogene floral assemblages around epicontinental seas and straits in Northern Central Eurasia : proxies for climatic and paleogeographic evolution

Paleogene connection of Tethyan and Paleoarctic water masses and biotas was largely enhanced by a N-S trending epicontinental seaway in northern Central Eurasia, which extended from the Aral Sea to the Amerasian deep basin of the Paleoarctic. This seaway enabled warm waters to impinge into polar latitudes, being a kind of "radiator" for the Arctic. Its closure had immediate effect on climatic conditions and terrestrial flora in the Arctic and entire North Eurasia. The Kara and West Siberian epicontinental seas, which were the major components of this N-S trending seaway, were connected to adjacent oceanic basins by a system of straits. Opening, closure, narrowing and widening of these straits in the Early Cenozoic determined the evolution of the marine ecosystems and current development, as well as the related depositional processes and biota (especially flora). The evolution of these straits also influenced on the Northern Hemisphere climatic fluctuations that took place during the Paleogene transition from a warm to a colder paleoclimatic state of the Earth system

The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability

We define a quadratic form which gives an obstruction to embedding $N^{4k+2} \subset \R^{6k+4}$ of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove that no 14-connected (resp. 30-connected) stably parallelizable manifold $N^{30}$ (resp. $N^{62}$) with Arf-Kervaire invariant one is smoothly embeddable into $\R^{36}$ (resp. $\R^{83}$)

Late Paleocene Flora of the Northern Alaska Peninsula: The Role of Transberingian Plant Migrations and Climatic Change

For the first time, the Late Sagwon Flora is described from the upper beds of the Prince Creek Formation (Upper Paleocene) at the Sagavanirktok River (northern Alaska Peninsula). The flora is dominated by the angiosperm Tiliaephyllum brooksense Moiseeva et Herman sp. nov. and conifer Metasequoia occidentalis (Newb.) Chaney. The Late Sagwon Flora is most similar to the Danian or Danian-Selandian flora from the middle part of the Upper Tsagayan Subformation (Amur Region) and lower part of the Wuyun Formation (Heilongjiang Province, China). This similarity allows us to hypothesize that the genus Tiliaephyllum, which dominated in the Late Tsagayan Flora, migrated via the Bering Land Bridge from southern paleolatitudes of the Far East to high latitudes of the Arctic Pacific, due to the progressively warming climate of the Paleocene. Additional new angiosperm species are described from the Late Sagwon Flora: Archeampelos mullii Moiseeva et Herman sp. nov., Tiliaephyllum brooksense Moiseeva et Herman sp. nov., and Dicotylophyllum sagwonicum Moiseeva et Herman sp. nov

Early to middle Eocene history of the Arctic Ocean from Nd-Sr isotopes in fossil fish debris, Lomonosov Ridge

Strontium and neodymium radiogenic isotope ratios in early to middle Eocene fossil fish debris (ichthyoliths) from Lomonosov Ridge (Integrated Ocean Drilling Program Expedition 302) help constrain water mass compositions in the Eocene Arctic Ocean between ∼55 and ∼45 Ma. The inferred paleodepositional setting was a shallow, offshore marine to marginal marine environment with limited connections to surrounding ocean basins. The new data demonstrate that sources of Nd and Sr in fish debris were distinct from each other, consistent with a salinity-stratified water column above Lomonosov Ridge in the Eocene. The 87Sr/86Sr values of ichthyoliths (0.7079–0.7087) are more radiogenic than Eocene seawater, requiring brackish to fresh water conditions in the environment where fish metabolized Sr. The 87Sr/86Sr variations probably record changes in the overall balance of river Sr flux to the Eocene Arctic Ocean between ∼55 and ∼45 Ma and are used here to reconstruct surface water salinity values. The ɛNd values of ichthyoliths vary between −5.7 and −7.8, compatible with periodic (or intermittent) supply of Nd to Eocene Arctic intermediate water (AIW) from adjacent seas. Although the Norwegian-Greenland Sea and North Atlantic Ocean were the most likely sources of Eocene AIW Nd, input from the Tethys Sea (via the Turgay Strait in early Eocene time) and the North Pacific Ocean (via a proto-Bering Strait) also contributed

An extreme case of plant-insect co-diversification: figs and fig-pollinating wasps

It is thought that speciation in phytophagous insects is often due to colonization of novel host plants, because radiations of plant and insect lineages are typically asynchronous. Recent phylogenetic comparisons have supported this model of diversification for both insect herbivores and specialized pollinators. An exceptional case where contemporaneous plant insect diversification might be expected is the obligate mutualism between fig trees (Ficus species, Moraceae) and their pollinating wasps (Agaonidae, Hymenoptera). The ubiquity and ecological significance of this mutualism in tropical and subtropical ecosystems has long intrigued biologists, but the systematic challenge posed by >750 interacting species pairs has hindered progress toward understanding its evolutionary history. In particular, taxon sampling and analytical tools have been insufficient for large-scale co-phylogenetic analyses. Here, we sampled nearly 200 interacting pairs of fig and wasp species from across the globe. Two supermatrices were assembled: on average, wasps had sequences from 77% of six genes (5.6kb), figs had sequences from 60% of five genes (5.5 kb), and overall 850 new DNA sequences were generated for this study. We also developed a new analytical tool, Jane 2, for event-based phylogenetic reconciliation analysis of very large data sets. Separate Bayesian phylogenetic analyses for figs and fig wasps under relaxed molecular clock assumptions indicate Cretaceous diversification of crown groups and contemporaneous divergence for nearly half of all fig and pollinator lineages. Event-based co-phylogenetic analyses further support the co-diversification hypothesis. Biogeographic analyses indicate that the presentday distribution of fig and pollinator lineages is consistent with an Eurasian origin and subsequent dispersal, rather than with Gondwanan vicariance. Overall, our findings indicate that the fig-pollinator mutualism represents an extreme case among plant-insect interactions of coordinated dispersal and long-term co-diversification