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On ${\rm PL}$ de Rham theory and rational homotopy type


About this Title

A. K. Bousfield and V. K. A. M. Gugenheim

Publication: Memoirs of the American Mathematical Society
Publication Year 1976: Volume 8, Number 179
ISBNs: 978-0-8218-2179-4 (print); 978-1-4704-0826-8 (online)
DOI: http://dx.doi.org/10.1090/memo/0179
MathSciNet review: 0425956

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Table of Contents


Chapters

  • 1. The simplicial algebra $v$
  • 2. The polynomial de Rham theory
  • 3. Multiplicative structure and the Eilenberg-Moore theorem
  • 4. A Quillen homotopy theory for DG algebras
  • 5. Function spaces for DG algebras
  • 6. The homotopy relation for DG algebras
  • 7. Minimal DG algebras
  • 8. The de Rham functors and their adjoints
  • 9. The Sullivan-de Rham equivalence theorem
  • 10. Proof of the Sullivan-de Rham equivalence theorem
  • 11. The Sullivan-de Rham localization and homotopy theorems
  • 12. Extensions of the Sullivan-de Rham theorems
  • Appendix
  • 13. Polynomial de Rham theory for simplicial complexes
  • 14. Another proof of 2.2
  • 15. Sullivan homotopies are homotopic in DASH
  • 16. Minimal algebras for spaces with \lq\lq{nice}\rq\rq cohomology
American Mathematical Society