Solomon Lefschetz

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Lefschetz, Solomon


Born Sept. 3, 1884, in Moscow. American mathematician.

Lefschetz was appointed a professor at Princeton University in 1924. He is the author of studies on algebraic geometry (theory of multidimensional algebraic manifolds involving substantial application of topological methods). In topology, Lefschetz, together with H. Hopf, created the general theory of the intersection of cycles in manifolds and is the originator of the algebraic theory of continuous mappings.


In Russian translation:
Algebraicheskaia topologiia. Moscow, 1949.
Geometricheskaia teoriia differentsial’nykh uravnenii. Moscow, 1961.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The basic fixed-point index of f/p was constructed in [8], and called there the homotopy Lefschetz index, as an element
and consequently, for [phi]: X [??] Y, we define the generalized Lefschetz number [LAMBDA]([phi]) of [phi] by letting
He covers dynamics, dimensional groups, the complexes of an s/u-bijective factor map, the double complexes of an s/u-bijective pair, a Lefschetz formula, examples, and questions.
Lefschetz, Stability of Nonlinear Control Systems, Academic Press, New York, NY, USA, 1965.
Stanley, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J.
Lefschetz, Stability by Liapunov's Direct Method, Academic Press, New York, NY, USA, 1961.
Abstract: The aim of this paper is to prove the Lefschetz fixed point theorem for random multivalued compact absorbing contractions on absolute neighbourhood multiretracts.
Deitmar, Generalised Selberg zeta functions and a conjectural Lefschetz formula, in Multiple Dirichlet series, automorphic forms, and analytic number theory, 177 190, Proc.
The invariants of dynamical systems are described in terms of the traces of powers of integer matrices, for example in studying the Lefschetz numbers [18].
Also appropriate for physicists, the advanced mathematics textbook describes the Standard Model of elementary particles, a spectral realization of the zeros of the Riemann zeta function, quantum statistical mechanical systems, and a cohomological Lefschetz trace formula.