Solomon Lefschetz

THE ROLE OF ALGEBRA IN TOPOLOGYf BY SOLOMON LEFSCHETZ

Solomon Lefschetz an Appreciation in Memoriam by Lawrence Markus

Solomon Lefschetz began and ended his scientific career as a theoretical engineer. In between, he accomplished the work of several lifetimes of creative foundational research in algebraic geometry and topology, complemented by important contributions to such diverse fields of mathematics as differential equations, control theory, and nonlinear mechanics. In addition to his fundamental mathemati...

Manifolds with a Boundary and Their Trans- Formations*

This is the continuation of the paper which appeared in the January, 1926, number of these Transactions.! Its chief object is to extend to an Mn with a boundary the results already obtained for transformations of manifolds without boundary. To these already treated in full we devote a few pages chiefly to elucidate and simplify certain points of importance for the extension. We have succeeded i...

Examples of Non-kähler Hamiltonian Circle Manifolds with the Strong Lefschetz Property

In this paperwe construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counter examples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz c...

Examples That the Strong Lefschetz Property Does Not Survive Symplectic Reduction

In this paper we construct a family of six-dimensional compact non-Kähler Hamiltonian S-manifolds, each of which satisfies the strong Lefschetz property itself but nevertheless has a non-Lefschetz symplectic quotient. This provides the first known counter examples to the question whether the strong Lefschetz property descends to the symplectic quotient. In addition we also show how to vary our ...