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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lie coalgebras and rational homotopy theory II: Hopf invariants


Authors: Dev Sinha and Ben Walter
Journal: Trans. Amer. Math. Soc. 365 (2013), 861-883
MSC (2010): Primary 55P62; Secondary 16E40, 55P48
Published electronically: September 25, 2012
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Abstract: 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 $ \textup {Hom}(\pi _* X, {\mathbb{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.


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Additional Information

Dev Sinha
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: dps@math.uoregon.edu

Ben Walter
Affiliation: Department of Mathematics, Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, KKTC, Mersin 10 Turkey
Email: benjamin@metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05654-6
PII: S 0002-9947(2012)05654-6
Keywords: Hopf invariants, Lie coalgebras, rational homotopy theory, graph cohomology
Received by editor(s): August 7, 2010
Received by editor(s) in revised form: April 28, 2011
Published electronically: September 25, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.