An-LIFTINGS INTO POSTNIKOV TOWERS

Postnikov Towers of Commutative S-algebras

The plus construction, Postnikov towers and universal central module extensions

Given a connected space X, we consider the effect of Quillen’s plus construction on the homotopy groups of X in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequence AX → X → X+, we explain the contribution of πnX to πnX +, πn+1X + and πnAX, πn+1AX explicitly in terms of the low dimensional homology of πnX regarded as a module over π1X. Key ing...

Postnikov Towers and Gottlieb Groups of Orbit Spaces

Let X be a 1-connected space with the homotopy type of a CW -space and H a finite group acting freely on X by homeomorphisms homotopic to the identity. We prove that lkη∗Gk(X) ⊆ Gk(X/H) for all k > 1 and some estimated positive integer lk which depends on k, where Gk is the k′th Gottlieb group and η : X → X/H is the quotient map to the orbit space X/H. We show that lk is independent of k for X ...

Liftings of Holomorphic Maps into Teichmüller Spaces

We study liftings of holomorphic maps into some Teichmüller spaces. We also study the relationship between universal holomorphic motions and holomorphic lifts into Teichmüller spaces of closed sets in the Riemann sphere.

Liftings and Quasi-Liftings of DG Modules

We prove lifting results for DG modules that are akin to Auslander, Ding, and Solberg’s famous lifting results for modules. Introduction Convention. Throughout this paper, let R be a commutative noetherian ring. Hochster famously wrote that “life is really worth living” in a Cohen-Macaulay ring [7]. For instance, if R is Cohen-Macaulay and local with maximal regular sequence t, then R/(t) is ar...