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This book introduces a new point-set level approach to stable homotopy theory that has
already had many applications and promises to have a lasting impact on the subject. Given …

Quadratic refinements of the intersection pairing on a Riemann surface appear to have two
mathematical origins: one in complex function theory dating back to Riemann in the 1870's …

The last few years have seen a revolution in our understanding of the foundations of stable
homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy …

Categorification is the process of finding category-theoretic analogs of set-theoretic concepts
by replacing sets with categories, functions with functors, and equations between functions …

We apply ideas from commutative algebra, and Morita theory to algebraic topology using
ring spectra. This allows us to prove new duality results in algebra and topology, and to view …

Modular forms appear in many facets of mathematics, and have played important roles in
geometry, mathematical physics, number theory, representation theory, topology, and other …

The study of symmetries on spaces has always been a major part of algebraic and
geometric topology, but the systematic homotopical study of group actions is relatively …

Let G be a finite extension of a torus. Working with highly structured ring and module
spectra, let M be any module over MU; examples include all of the standard homotopical MU …

We give the first examples of finite groups G such that the Chow ring of the classifying space
BG depends on the base field, even for fields containing the algebraic closure of ℚ. As a …