1 results
The affirmative answer to Singer's conjecture on the algebraic transfer of rank four
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 5 / October 2023
- Published online by Cambridge University Press:
- 23 August 2022, pp. 1529-1542
- Print publication:
- October 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
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 $4.$
