A classification of secondary cohomology operations

The Factorization of Cyclic Reduced Powers by Secondary Cohomology Operations.

I Lewin, J. C., Science, 112, 652 (1950). 2 In the experiments reported here, cultures were grown on minimal medium plus sodium acetate (0.2 gm per 100 ml). The minimal medium, described in Levine, R. P., and Ebersold, W. T., Zeit. Vererbungs., 89, 632 (1958), was altered by a fivefold increase in the concentration of Beijerinck's solution. 3 Arnon, D. I., Plant Physiol., 24, 1 (1949). 4The aut...

Secondary Steenrod Operations in Cohomology of Infinite-Dimensional Projective Spaces

The important role of the Steenrod operations Sq in the description of the cohomology of topological spaces, the calculation of various spectral sequences, and the study of homotopy properties of topological spaces and their continuous maps is well known [1, 2]. Projective spaces, in particular RP∞ and CP∞ , play a special role in the construction of Steenrod operations and their computation. I...

Cohomology operations and algebraic geometry

This manuscript is based on a ten hours series of seminars I delivered in August of 2003 at the Nagoya Institute of Technology as part of the workshop on homotopy theory organized by Norihiko Minami and following the Kinosaki conference in honor of Goro Nishida. One of the most striking applications of homotopy theory in “exotic” contexes is Voevodsky’s proof of the Milnor Conjecture. This conj...

Robot Motion Planning, Weights of Cohomology Classes, and Cohomology Operations

The complexity of algorithms solving the motion planning problem is measured by a homotopy invariant TC(X) of the configuration space X of the system. Previously known lower bounds for TC(X) use the structure of the cohomology algebra of X. In this paper we show how cohomology operations can be used to sharpen these lower bounds for TC(X). As an application of this technique we calculate explic...

Stable Operations in Generalized Cohomology