LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY II: HOPF INVARIANTS

Date

2013-02-01

Author

Sinha, Dev
Walter, Ben

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We develop a new framework which resolves the homotopy periods problem. We start with integer-valued homotopy periods defined explicitly from the classic bar construction. We then work rationally, where we use the Lie coalgebraic bar construction to get a sharp model for Hom(pi*X,Q) for simply connected X. We establish geometric interpretations of these homotopy periods, to go along with the good formal properties coming from the Koszul-Moore duality framework. We give calculations, applications, and relationships with the numerous previous approaches.

Subject Keywords

Hopf invariants, Lie coalgebras, Rational homotopy theory, Graph cohomology

URI

https://hdl.handle.net/11511/64808

Journal

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Collections

Natural Sciences and Mathematics, Article

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Citation Formats

D. Sinha and B. Walter, “LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY II: HOPF INVARIANTS,” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 861–883, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64808.