Abstract This is an expository article without any claim of originality. We give a complete and self-contained account the Gromov–Lawson–Chernysh surgery theorem for positive scalar curvature metrics.

We first prove that for all compact metrizable spaces, there exists a topological embedding of the space into each sets metric spaces which are connected, path-connected, geodesic, or CAT(0), in Gromov–Hausdorff with finite prescribed values. As its application, we show above path-connected and their non-empty open subsets have infinite dimension. By same method, also set proper CAT(0) is dimen...

The article is devoted to the review of IV Green Readings held at Kostroma State University and analysis actual problems modern regional lexicography considered during work this scientific event. assesses ascetic activity A.V. Gromov, a well-known connoisseur folk culture language, dialectologist lexicographer, teacher ethnographer. ideas heritage Gromov in context dialectography reveals vitali...

We prove a conjecture of Artur Elezi [4] in a generalized form suggested by Givental [5]. Namely, our main result relates genus-0 Gromov–Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold. When the base is the point, a new proof of mirror theorems by A. Givental [6] and H. Iritani [9] for toric manifolds is obtained. 1 Formulations ...

A kinetic chemistry tagging technique and its application to modelling the stable isotopic composition of atmospheric trace gases S. Gromov, P. Jöckel, R. Sander, and C. A. M. Brenninkmeijer Atmospheric Chemistry Department, Max Planck Institute for Chemistry, P.O. Box 3060, 55020 Mainz, Germany now at: Deutsches Zentrum für Luft-und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaf...

Let V be a smooth, projective, convex variety. We define tautological ψ and κ classes on the moduli space of stable maps M0,n(V ), give a (graphical) presentation for these classes in terms of boundary strata, derive differential equations for the generating functions of the Gromov-Witten invariants of V twisted by these tautological classes, and prove that these intersection numbers are comple...

The (small) quantum cohomology ring of a Grassmann variety encodes the enumerative geometry of rational curves in this variety. By using degeneracy loci formulas on quot schemes, Bertram has proved quantum Pieri and Giambelli formulas which give a complete description of the quantum cohomology ring. In this talk I will present elementary new proofs of these results which rely only on the defini...