Homotopy pullback of An-spaces and its applications to An-types of gauge groups

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalTopology and its Applications
Volume187
DOIs
Publication statusPublished - Jun 1 2015
Externally publishedYes

Fingerprint

Pullback
Gauge Group
Homotopy
CW-complex
Bundle
Form
Review

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Homotopy pullback of An-spaces and its applications to An-types of gauge groups. / Tsutaya, Mitsunobu.

In: Topology and its Applications, Vol. 187, 01.06.2015, p. 1-25.

Research output: Contribution to journalArticle

@article{bccfeaaeaa884cfbbcf3e1967aaf8d6b,
title = "Homotopy pullback of An-spaces and its applications to An-types of gauge groups",
abstract = "We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.",
author = "Mitsunobu Tsutaya",
year = "2015",
month = "6",
day = "1",
doi = "10.1016/j.topol.2015.02.014",
language = "English",
volume = "187",
pages = "1--25",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",

}

TY - JOUR

T1 - Homotopy pullback of An-spaces and its applications to An-types of gauge groups

AU - Tsutaya, Mitsunobu

PY - 2015/6/1

Y1 - 2015/6/1

N2 - We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.

AB - We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.

UR - http://www.scopus.com/inward/record.url?scp=84924529799&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924529799&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2015.02.014

DO - 10.1016/j.topol.2015.02.014

M3 - Article

AN - SCOPUS:84924529799

VL - 187

SP - 1

EP - 25

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

ER -