Group actions on contractible 2-complexes II

Kevin Piterman; Iván Sadofschi Costa

doi:10.48550/arXiv.2102.11459

Group actions on contractible 2-complexes II

Kevin Piterman, Iván Sadofschi Costa

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

1 Citation (Scopus)

Abstract

In this second part we prove that, if G is one of the groups PSL2(q) with q>5 and q≡5(mod24) or q≡13(mod24), then the fundamental group of every acyclic 2-dimensional, fixed point free and finite G-complex admits a nontrivial representation in a unitary group U(m). This completes the proof of the following result: every action of a finite group on a finite and contractible 2-complex has a fixed point.

Original language	English
Pages (from-to)	563-570
Number of pages	8
Journal	Inventiones Mathematicae
Volume	242
Issue number	2
DOIs	https://doi.org/10.48550/arXiv.2102.11459 https://doi.org/10.1007/s00222-025-01363-8
Publication status	Published - 4 Sept 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

Access to Document

10.48550/arXiv.2102.11459Licence: Unspecified
10.1007/s00222-025-01363-8

Handle.net

Persistent link

Cite this

@article{eaedfedabe2f4854b5ce77d47855ea48,

title = "Group actions on contractible 2-complexes II",

abstract = "In this second part we prove that, if G is one of the groups PSL2(q) with q>5 and q≡5(mod24) or q≡13(mod24), then the fundamental group of every acyclic 2-dimensional, fixed point free and finite G-complex admits a nontrivial representation in a unitary group U(m). This completes the proof of the following result: every action of a finite group on a finite and contractible 2-complex has a fixed point.",

author = "Kevin Piterman and {Sadofschi Costa}, Iv{\'a}n",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.",

year = "2025",

month = sep,

day = "4",

doi = "10.48550/arXiv.2102.11459",

language = "English",

volume = "242",

pages = "563--570",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Group actions on contractible 2-complexes II

AU - Piterman, Kevin

AU - Sadofschi Costa, Iván

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025/9/4

Y1 - 2025/9/4

N2 - In this second part we prove that, if G is one of the groups PSL2(q) with q>5 and q≡5(mod24) or q≡13(mod24), then the fundamental group of every acyclic 2-dimensional, fixed point free and finite G-complex admits a nontrivial representation in a unitary group U(m). This completes the proof of the following result: every action of a finite group on a finite and contractible 2-complex has a fixed point.

AB - In this second part we prove that, if G is one of the groups PSL2(q) with q>5 and q≡5(mod24) or q≡13(mod24), then the fundamental group of every acyclic 2-dimensional, fixed point free and finite G-complex admits a nontrivial representation in a unitary group U(m). This completes the proof of the following result: every action of a finite group on a finite and contractible 2-complex has a fixed point.

UR - http://www.scopus.com/inward/record.url?scp=105015406401&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2102.11459

DO - 10.48550/arXiv.2102.11459

M3 - Article

SN - 0020-9910

VL - 242

SP - 563

EP - 570

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -

Group actions on contractible 2-complexes II

Abstract

Bibliographical note

Access to Document

Handle.net

Other files and links

Embargoed Document

Fingerprint

Cite this