Enhanced AA-infinity obstruction theory

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of truncated minimal A-infinity algebra structures. We also consider the Bousfield-Kan spectral sequence for the moduli space of A-infinity algebras. We compute up to the second page, terms and differentials, of these spectral sequences in terms of Hochschild cohomology.Comment: 42 pages, color figure

Maltsiniotis's first conjecture for K_1

We show that K_1 of an exact category agrees with K_1 of the associated triangulated derivator. More generally we show that K_1 of a Waldhausen category with cylinders and a saturated class of weak equivalences coincides with K_1 of the associated right pointed derivator.Comment: 23 pages, the main results have been generalize

Cylinders for non-symmetric DG-operads via homological perturbation theory

We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity operad, yields the operad parametrizing A-infinity maps whose linear part is the identity. We also compute some other examples with non-trivial operations in arities 1 and 0.Comment: 33 page

Unital associahedra

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A-infinity algebras of Fukaya-Oh-Ohta-Ono.Comment: 22 pages, EPS color figure