The homology of iterated loop spaces

By V.A.Smirnov. 2000

163 citations recorded by the source corpus.

In recent years, to solve various problems in Algebraic Topology it has been necessary to consider more and more complicated structures on the singular chain complex C∗(X) of a topological space X and its homology H∗(X). One of the most difficult problem is the problem of calculating the homology groups of iterated loop spaces. The first steps toward solving this problem were made by J.F.Adams, [1]. To calculate the homology H∗(ΩX) of the loop space ΩX of a topological space X he introduced the notion of the cobar construction FK on a coalgebra K. Recall that a chain complex K is called a coalgebra if there is given a chain mapping ∇:K → K ⊗K satisfying the associativity relation

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2e6b883f6985b0a820a490637aa001a4f37c97b

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

On the other side of the bialgebra of chord diagrams (2004, unknown): “[1, 7, 8, 10, 20, 22, 23, 26], and as consequence of Theorems 10.”
More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, background): “The calculation of H∗(BPL; Fp) at all primes p is described in [78, 29], but that is another story.”