On algebras of holomorphic functions of a given type

We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert-Schmidt bounded type, are locally $m$-convex Fr\'echet algebras. We prove that the spectrum of these algebras has a natural analytic structure, which we use to characterize the envelope of holomorphy. We also show a Cartan-Thullen type theorem.Comment: 30 page

Perspective

Why do metropolitan areas need to ensure that their universities, corporations, and independent laboratories conduct abundant, top-flight research and development? Why would Southern Nevada do well to build up its research capability, particularly in the sciences and engineering? The answer has to do with what has increasingly emerged as an unavoidable syllogism of economic competitiveness. To put it simply: Prosperity depends on productivity; productivity depends heavily on innovation, and innovation depends heavily on research and development. The bottom line: A region thin on R&D is not likely to be innovative, and if it is not innovative, it will probably not flourish

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