On the minimal number of critical points of functions on h-cobordisms

Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.Comment: 7 pages, Late

Grothendieck groups and a categorification of additive invariants

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic

On Thom spectra, orientability, and cobordism

For many years, algebraic topology rests on three legs: 'ordinary' cohomology, K-theory, and cobordism. This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra. From the Foreword by Haynes Miller The author has also performed a service to the history of science in this book, giving detailed attributions. This s

Minimal atlases of closed symplectic manifolds

info:eu-repo/semantics/publishe

Lusternik--Schnirelmann theory on general spaces

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Gas hydrates impact on corrosion of the well flow lines material

Purpose: Determination of regularities of joint action of mechanical stresses, formation water and hydrate formation on corrosion of material of flow pipelines. Design/methodology/approach: According to the analysis of reservoir water of the investigated deposits, it was found that the main corrosive component is soluble chlorides. Proposed for corrosion and corrosion-mechanical tests of 6 model environments. An estimation of the influence of stress concentration, depending on the defects of the inner wall of the pipe, was carried out, and the nominal local stresses in the pipeline was carried. Findings: The basic regularities of influence of stress and hydration formation on corrosion and localization of corrosion processes and on the kinetics of deformation of samples are described. For samples made of steel 20 and 17GS, an increase in the velocity of general and local corrosion for samples sustained in the gas hydrate was observed compared to the control results obtained, the coefficient of influence of the gas hydrate on corrosion was calculated. Research limitations/implications: The obtained results are valid for thermobaric operating conditions of well flow lines. Practical implications: The data obtained in the work on the patterns of corrosion processes and the impact of hydrate formation on them will allow to identify potentially dangerous areas of flow lines and prevent emergencies. Originality/value: Based on the analysis of the geometric dimensions of the defects, the effective stress concentration coefficients are calculated, and it is shown that the stresses in the vicinity of corrosion defects in normal operating modes range from 164 to 545 MPa