A commutative model for PL compactly supported cohomology in characteristic zero

2019/07/09 by Tom Sutton, Sutton, Tom
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1907.04454

openalex publication_date 2019/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that that classical rational homotopy theory in the sense of Sullivan [6] can be extended compactly supported setting. This presents a simplicial version of the compactly supported de Rham complex in characteristic zero, and proving that it models singular compactly supported cohomology. This presents new avenues of possible study in proper homotopy theory, and further extensions of the ideas within the classical literature of Quillen [5] and Sullivan.

Citations

• Long exact sequences for de Rham cohomology of diffeological spaces

Related

• Rational homotopy theory: a brief introduction
• Rational Homotopy Type of Complements of Submanifold Arrangements
• A note on non-simply connected rational homotopy models
• André-Quillen cohomology and rational homotopy of function spaces
• Rigid Cohomology and de Rham-Witt complexes