What question did this study set out to answer?

The research aims to understand the relative Gelfand–Fuks cohomology using rational homotopy theory.

April 19, 2026Open Access

A note on relative Gelfand–Fuks cohomology of spheres

Key Points

The research aims to understand the relative Gelfand–Fuks cohomology using rational homotopy theory.
Utilized Haefliger's method involving rational homotopy theory
Examined smooth vector fields
Performed computations in low cohomological degrees
Demonstrated injectivity into the relative Gelfand–Fuks cohomology
Established agreement between relative Gelfand–Fuks and smooth cohomology
Provided specific computations in low degrees

Abstract

Abstract We study the Gelfand–Fuks cohomology of smooth vector fields on relative to following a method of Haefliger that uses tools from rational homotopy theory. In particular, we show that injects into the relative Gelfand–Fuks cohomology which corrects a claim by Haefliger. Moreover, for the relative Gelfand–Fuks cohomology agrees with the smooth cohomology of and we provide a computation in low degrees.

A note on relative Gelfand–Fuks cohomology of spheres

Key Points

Abstract

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