Abstract
The relationship between Yoneda Ext algebras of local rings and the homology rings of loop spaces on simply connected CW complexes has been observed by several authors [7] [8] [11] [16]. Most of the work has been done over characteristic zero. In this paper we will use the Adams-Hilton construction [2] to understand this connection over arbitrary characteristics.
Four consequences of the resulting theory are especially noteworthy. The concept of formal spaces is generalized to non-zero characteristics. The Eilenberg-Moore spectral sequence for the homology of the loop space has E2 ≈ E∞ as algebras for many spaces, and as algebras "up to sign" for others. We compute the Poincaré series and Pontrjagin structures for the loop space on a Λ-wedge (to be defined) of suspensions. Finally, we observe that all Ext algebras of commutative monomial k-algebras occur as the Pontrjagin rings of loop spaces.
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Anick, D.J. (1984). Connections between Yoneda and Pontrjagin algebras. In: Madsen, I.H., Oliver, R.A. (eds) Algebraic Topology Aarhus 1982. Lecture Notes in Mathematics, vol 1051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075575
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DOI: https://doi.org/10.1007/BFb0075575
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