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- Title
The affirmative answer to Singer's conjecture on the algebraic transfer of rank four.
- Authors
Phúc, Đặng Võ
- Abstract
During the last decades, the structure of mod-2 cohomology of the Steenrod ring $\mathscr {A}$ became a major subject in Algebraic topology. One of the most direct attempt in studying this cohomology by means of modular representations of the general linear groups was the surprising work [ Math. Z. 202 (1989), 493–523] by William Singer, which introduced a homomorphism, the so-called algebraic transfer , mapping from the coinvariants of certain representation of the general linear group to mod-2 cohomology group of the ring $\mathscr A.$ He conjectured that this transfer is a monomorphism. In this work, we prove Singer's conjecture for homological degree $4.$
- Subjects
ALGEBRAIC topology; LOGICAL prediction; GROUP rings; MATHEMATICS; HOMOMORPHISMS
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2023, Vol 153, Issue 5, p1529
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/prm.2022.57