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This book is intended for graduate students and research mathematicians working in classical linear algebraic
This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.
This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.
Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple intersections of a large class of strongly symmetric L vy processes in $R DEGREESm$, $m=1,2$. In $R DEGREES2$ these include Brownian motion and stable processes of index greater than 3/2, as well as many processes in their domains of attraction. In $R DEGREES1$ these include stable processes of index $3/4
This book is intended for graduate students and research mathematicians working in logic and foundations
This book is intended for graduate students and research mathematicians working in group theory and generalizations.
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
This book is intended for graduate students and research mathematicians working in algebraic geometry
This book is intended for graduate students and research mathematicians interested in mathematical logic and foundations.
We develop the theory of compactness of maps between toposes, together with associated notions of separatedness. This theory is built around two versions of "propriety" for topos maps, introduced here in a parallel fashion. The first, giving what we simply call "proper" maps, is a relatively weak condition due to Johnstone. The second kind of proper maps, here called "tidy", satisfy a stronger condition due to Tierney and Lindgren. Various forms of the Beck-Chevalley condition for (lax) fibered product squares of toposes play a central role in the development of the theory. Applications include a version of the Reeb stability theorem for toposes, a characterization of hyperconnected Hausdorff toposes as classifying toposes of compact groups, and of strongly Hausdorff coherent toposes as classifiying toposes of profinite groupoids. Our results also enable us to develop further particular aspects of the factorization theory of geometric morphisms studied by Johnstone. Our final application is a (so-called lax) descent theorem for tidy maps between toposes. This theorem implies the lax descent theorem for coherent toposes, conjectured by Makkai and proved earlier by Zawadowski.