Directed diagrammatic reducibility

Jens Harlander; Stephan Rosebrock

doi:10.1016/j.topol.2020.107307

Directed diagrammatic reducibility

Jens Harlander, Stephan Rosebrock

Mathematics Department

Karlsruhe University of Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given. Results concerning asphericity and π₁-injectivity of subcomplexes are shown. We generalize the Corson-Trace characterization of diagrammatic reducibility to directed diagrammatic reducibility. We compare diagrammatic reducibility of relative presentations to directed diagrammatic reducibility. Classical tools for showing diagrammatic reducibility, such as the weight test, the max/min test, and small cancellation techniques are adapted to directed diagrammatic reducibility. The paper ends with some applications to labeled oriented trees.

Original language	English
Article number	107307
Journal	Topology and its Applications
Volume	282
DOIs	https://doi.org/10.1016/j.topol.2020.107307
State	Published - 15 Aug 2020

Keywords

2-Complex
Asphericity
Diagrammatic reducibility
Group-presentation
Weight test

Access to Document

10.1016/j.topol.2020.107307

Cite this

@article{0b005c0277fe4f138568c6d0697a4e51,

title = "Directed diagrammatic reducibility",

abstract = "We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given. Results concerning asphericity and π1-injectivity of subcomplexes are shown. We generalize the Corson-Trace characterization of diagrammatic reducibility to directed diagrammatic reducibility. We compare diagrammatic reducibility of relative presentations to directed diagrammatic reducibility. Classical tools for showing diagrammatic reducibility, such as the weight test, the max/min test, and small cancellation techniques are adapted to directed diagrammatic reducibility. The paper ends with some applications to labeled oriented trees.",

keywords = "2-Complex, Asphericity, Diagrammatic reducibility, Group-presentation, Weight test",

author = "Jens Harlander and Stephan Rosebrock",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = aug,

day = "15",

doi = "10.1016/j.topol.2020.107307",

language = "English",

volume = "282",

}

TY - JOUR

T1 - Directed diagrammatic reducibility

AU - Harlander, Jens

AU - Rosebrock, Stephan

PY - 2020/8/15

Y1 - 2020/8/15

N2 - We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given. Results concerning asphericity and π1-injectivity of subcomplexes are shown. We generalize the Corson-Trace characterization of diagrammatic reducibility to directed diagrammatic reducibility. We compare diagrammatic reducibility of relative presentations to directed diagrammatic reducibility. Classical tools for showing diagrammatic reducibility, such as the weight test, the max/min test, and small cancellation techniques are adapted to directed diagrammatic reducibility. The paper ends with some applications to labeled oriented trees.

AB - We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given. Results concerning asphericity and π1-injectivity of subcomplexes are shown. We generalize the Corson-Trace characterization of diagrammatic reducibility to directed diagrammatic reducibility. We compare diagrammatic reducibility of relative presentations to directed diagrammatic reducibility. Classical tools for showing diagrammatic reducibility, such as the weight test, the max/min test, and small cancellation techniques are adapted to directed diagrammatic reducibility. The paper ends with some applications to labeled oriented trees.

KW - 2-Complex

KW - Asphericity

KW - Diagrammatic reducibility

KW - Group-presentation

KW - Weight test

UR - http://www.scopus.com/inward/record.url?scp=85086911537&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2020.107307

DO - 10.1016/j.topol.2020.107307

M3 - Article

AN - SCOPUS:85086911537

SN - 0166-8641

VL - 282

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 107307

ER -

Directed diagrammatic reducibility

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this