Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900407 | Transactions of A. Razmadze Mathematical Institute | 2017 | 7 Pages |
Abstract
Given a simply connected space X with polynomial cohomology Hâ(X;Z2), we calculate the loop cohomology algebra Hâ(ΩX;Z2) by means of the action of the Steenrod cohomology operation Sq1 on Hâ(X;Z2). This calculation uses an explicit construction of the minimal Hirsch filtered model of the cochain algebra Câ(X;Z2). As a consequence we obtain that Hâ(ΩX;Z2) is the exterior algebra if and only if Sq1 is multiplicatively decomposable on Hâ(X;Z2). The last statement in fact contains a converse of a theorem of A. Borel (Switzer, 1975, Theorem 15.60).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Samson Saneblidze,