Work

Rational and $p$-adic analogues of J. H. C. Whitehead's conjecture

Year: 2025

Type: article

Abstract: We show that subpresentations of aspherical prounipotent presentations over fields of characteristic zero and subpresentations of aspherical pro-$p$-presentations are aspherical. The results are regarded as affirmative answers to the rational and $p$-adic analogues of J. H. C. Whitehead conjecture. Methods of affine group schemes make it possible to unify the presentation for pro-$p$-groups and pro-unipotent groups in characteristic zero. This approach, in particular, allows us to put a rigour mathematical reason under the philosophy proposed by J.-P. Serre; applications of our results to the classical Whitehead's problem are discussed as well.

Source: Izvestiya Mathematics

DOI: 10.4213/im9597e

Author: Andrey Mikhovich

Institutions: Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4410373383

FWCI:

Cites: 43

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Related to: 10