Singular Cochains and rational Homotopy Type

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Title: Singular Cochains and rational Homotopy Type
Author: Kharebava, Zviad
Advisors: Tom Lada, Committee Chair
Abstract: Rational homotopy types of simply connected topological spaces have been classified by weak equivalence classes of commutative cochain algebras (Sullivan) and by isomorphism classes of minimal commutative $A_{infty}$-algebras (Kadeishvili). We classify rational homotopy types of the space $X$ by using the (non-commutative) singular cochain complex, $C^{ast}(X,Q)$, with additional structure given by the homotopies introduced by Baues, ${E_{1,k}}$ and ${F_{p,q}}$. We show that if we modify the resulting $B_{infty}$-algebra structure on this algebra by requiring that its bar construction be a Hopf algebra up to homotopy, then weak equivalence classes of such algebras classify rational homotopy types.
Date: 2004-03-31
Degree: PhD
Discipline: Mathematics

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