2021/10/02 by Đặng Võ Phúc, Phuc, Dang Vo · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #13A50 #55Q45 #55R12 #55S05 #55S10 #55T15 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2110.00763
openalex publication_date 2021/10/02 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28
Writing \mathbb A for the 2-primary Steenrod algebra, which is the algebra of stable natural endomorphisms of the mod 2 cohomology functor on topological spaces. Working at the prime 2, computing the cohomology of \mathbb A is an important problem of Algebraic topology, because it is the initial page of the Adams spectral sequence converging to stable homotopy groups of the spheres. A relatively efficient tool to describe this cohomology is the Singer algebraic transfer of rank n in [Math. Z. 202 (1989), 493-523], which passes from a certain subquotient of a divided power algebra to the cohomology of \mathbb A. Singer predicted that this transfer is a monomorphism, but this remains open for n≥ 4. This short note is to verify the conjecture in the ranks 4 and 5 and some generic degrees.