Right exact group completion as a transfinite invariant of homology equivalence

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Right exact group completion as a transfinite invariant of homology equivalence. / Ivanov, Sergei O.; Mikhailov, Roman.

In: Algebraic and Geometric Topology, Vol. 21, No. 1, 2021, p. 447-468.

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

BibTeX

@article{93079462b6eb4d53a9a2f6125c421c5d,

title = "Right exact group completion as a transfinite invariant of homology equivalence",

abstract = "We consider a functor from the category of groups to itself, G → Z∞G, that we call right exact Z -completion of a group. It is connected with the pro-nilpotent completion G by the short exact sequence 1 → lim1 MnG → Z∞G → G → 1, where MnG is nth Baer invariant of G. We prove that Z00(µ1X) is an invariant of homological equivalence of a space X. Moreover, we prove an analogue of Stallings' theorem: If G → G0 is a 2-connected group homomorphism, then Z∞G ^ Z∞G'. We give examples of 3-manifolds X and Y such that n1X ^ 7r17 but Z1^1X",

author = "Ivanov, {Sergei O.} and Roman Mikhailov",

year = "2021",

doi = "10.2140/agt.2021.21.447",

language = "English",

volume = "21",

pages = "447--468",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Geometry & Topology Publications",

number = "1",

}

RIS

TY - JOUR

T1 - Right exact group completion as a transfinite invariant of homology equivalence

AU - Ivanov, Sergei O.

AU - Mikhailov, Roman

PY - 2021

Y1 - 2021

N2 - We consider a functor from the category of groups to itself, G → Z∞G, that we call right exact Z -completion of a group. It is connected with the pro-nilpotent completion G by the short exact sequence 1 → lim1 MnG → Z∞G → G → 1, where MnG is nth Baer invariant of G. We prove that Z00(µ1X) is an invariant of homological equivalence of a space X. Moreover, we prove an analogue of Stallings' theorem: If G → G0 is a 2-connected group homomorphism, then Z∞G ^ Z∞G'. We give examples of 3-manifolds X and Y such that n1X ^ 7r17 but Z1^1X

AB - We consider a functor from the category of groups to itself, G → Z∞G, that we call right exact Z -completion of a group. It is connected with the pro-nilpotent completion G by the short exact sequence 1 → lim1 MnG → Z∞G → G → 1, where MnG is nth Baer invariant of G. We prove that Z00(µ1X) is an invariant of homological equivalence of a space X. Moreover, we prove an analogue of Stallings' theorem: If G → G0 is a 2-connected group homomorphism, then Z∞G ^ Z∞G'. We give examples of 3-manifolds X and Y such that n1X ^ 7r17 but Z1^1X

UR - http://www.scopus.com/inward/record.url?scp=85103036649&partnerID=8YFLogxK

U2 - 10.2140/agt.2021.21.447

DO - 10.2140/agt.2021.21.447

M3 - Article

AN - SCOPUS:85103036649

VL - 21

SP - 447

EP - 468

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 1

ER -

ID: 90651015