Ralph L. Cohen

Ralph L.Cohen
Barbara Kimball Browning Professor
in the School of Humanities and Sciences, Emeritus
Bass University Fellow in Undergraduate Education
Professor of Mathematics, Emeritus
Stanford University

Email: rlc@stanford.edu

Current CV

Current Publication list

Research interests

Algebraic and Differential Topology

Algebraic topological aspects of moduli spaces of Riemann surfaces,
gauge theoretic moduli spaces, holomorphic mapping spaces,
Loop spaces, loop groups, string topology.
K -theory, homotopy theory, homotopy theoretic aspects of symplectic topology

Click here for some of my recent papers.

During the last few years I have been in the process of compiling lecture notes from the many courses in Algebraic and Differential Topology that I've taught over the years, and turning them into a book. The focus of this book is the algebraic topology of manifolds, and will include such topics as intersection theory, immersions, embeddings, homotopy theory (including fibrations and cofibrations, spectral sequences, spectra and the Steenrod algebra), Morse theory (including moduli spaces of gradient flow lines), cobordism theory (including a calculation of unoriented and almost complex cobordism, a discussion of framed cobordism including framed surgery and the Kervaire invariant, and a discussion of the topology of cobordism categories), and bundle theory (including characteristic classes, and basic gauge theory).

The book's title is

"Bundles, Manifolds, and Homotopy"

and will soon be published in the "Graduate Studies in Mathematics" series of the American Mathematical Society. Click here for the latest version of the book. Version date: August 10, 2025.