Lie coalgebras and rational homotopy theory II: Hopf invariants
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- by Dev Sinha and Ben Walter PDF
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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 $\mathrm {Hom}(\pi _* X, {\mathbb Q})$ 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.References
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Additional Information
- Dev Sinha
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
- MR Author ID: 681577
- 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
- Received by editor(s): August 7, 2010
- Received by editor(s) in revised form: April 28, 2011
- Published electronically: September 25, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 861-883
- MSC (2010): Primary 55P62; Secondary 16E40, 55P48
- DOI: https://doi.org/10.1090/S0002-9947-2012-05654-6
- MathSciNet review: 2995376