Relative phantom maps and rational homotopy

Daisuke Kishimoto; Takahiro Matsushita

doi:10.1090/proc/15431

Relative phantom maps and rational homotopy

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

Abstract

We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the lim¹ and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.

Original language	English
Pages (from-to)	4029
Number of pages	1
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	9
DOIs	https://doi.org/10.1090/proc/15431
Publication status	Published - 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/15431

Cite this

@article{0f567b2411324cca892b93c5710ff621,

title = "Relative phantom maps and rational homotopy",

abstract = "We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the lim1 and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.",

author = "Daisuke Kishimoto and Takahiro Matsushita",

note = "Funding Information: Received by the editors October 17, 2019, and, in revised form, October 27, 2020. 2020 Mathematics Subject Classification. Primary 55P99; Secondary 55P62. Key words and phrases. Relative phantom map, phantom map, ratiotal homotopy. The authors were supported in part by JSPS KAKENHI No. 17K05248 and No. 19K14536. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",

year = "2021",

doi = "10.1090/proc/15431",

language = "English",

volume = "149",

pages = "4029",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "9",

}

TY - JOUR

T1 - Relative phantom maps and rational homotopy

AU - Kishimoto, Daisuke

AU - Matsushita, Takahiro

N1 - Funding Information: Received by the editors October 17, 2019, and, in revised form, October 27, 2020. 2020 Mathematics Subject Classification. Primary 55P99; Secondary 55P62. Key words and phrases. Relative phantom map, phantom map, ratiotal homotopy. The authors were supported in part by JSPS KAKENHI No. 17K05248 and No. 19K14536. Publisher Copyright: © 2021 American Mathematical Society

PY - 2021

Y1 - 2021

N2 - We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the lim1 and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.

AB - We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the lim1 and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.

UR - http://www.scopus.com/inward/record.url?scp=85111225646&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85111225646&partnerID=8YFLogxK

U2 - 10.1090/proc/15431

DO - 10.1090/proc/15431

M3 - Article

AN - SCOPUS:85111225646

VL - 149

SP - 4029

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -

Relative phantom maps and rational homotopy

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this