EQUIVARIANT TREES AND PARTITION COMPLEXES

Julia E. Bergner; Peter Bonventre; Maxine E. Calle; David Chan; Maru Sarazola

EQUIVARIANT TREES AND PARTITION COMPLEXES

Julia E. Bergner
, Peter Bonventre
, Maxine E. Calle
, David Chan
, Maru Sarazola

School of Mathematics

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

Abstract

We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen’s Theorems A and B, which are of independent interest.

Original language	English (US)
Pages (from-to)	501-536
Number of pages	36
Journal	Theory and Applications of Categories
Volume	45
State	Published - 2026

Bibliographical note

Publisher Copyright:
© Julia E. Bergner, Peter Bonventre, Maxine E. Calle, David Chan, and Maru Sarazola, 2026.

Keywords

equivariant homotopy theory
partition complexes
trees

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title = "EQUIVARIANT TREES AND PARTITION COMPLEXES",

abstract = "We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen{\textquoteright}s Theorems A and B, which are of independent interest.",

keywords = "equivariant homotopy theory, partition complexes, trees",

author = "Bergner, \{Julia E.\} and Peter Bonventre and Calle, \{Maxine E.\} and David Chan and Maru Sarazola",

note = "Publisher Copyright: {\textcopyright} Julia E. Bergner, Peter Bonventre, Maxine E. Calle, David Chan, and Maru Sarazola, 2026.",

year = "2026",

language = "English (US)",

volume = "45",

pages = "501--536",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

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TY - JOUR

T1 - EQUIVARIANT TREES AND PARTITION COMPLEXES

AU - Bergner, Julia E.

AU - Bonventre, Peter

AU - Calle, Maxine E.

AU - Chan, David

AU - Sarazola, Maru

N1 - Publisher Copyright: © Julia E. Bergner, Peter Bonventre, Maxine E. Calle, David Chan, and Maru Sarazola, 2026.

PY - 2026

Y1 - 2026

N2 - We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen’s Theorems A and B, which are of independent interest.

AB - We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen’s Theorems A and B, which are of independent interest.

KW - equivariant homotopy theory

KW - partition complexes

KW - trees

UR - https://www.scopus.com/pages/publications/105033671197

UR - https://www.scopus.com/pages/publications/105033671197#tab=citedBy

M3 - Article

AN - SCOPUS:105033671197

SN - 1201-561X

VL - 45

SP - 501

EP - 536

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

ER -

EQUIVARIANT TREES AND PARTITION COMPLEXES

Abstract

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