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Central Extensions of Simplicial Gro...

Niemeier, Michael.

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Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups./
Author:	Niemeier, Michael.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	100 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Contained By:	Dissertations Abstracts International82-05B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27995537
ISBN:	9798684653056

Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups.
Niemeier, Michael.

Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 100 p.

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--The Florida State University, 2020.

This item must not be sold to any third party vendors.

We show that path components of central extensions of a simplicial group G by a simplicial abelian group A are in bijection with the homotopy classes of maps between classifying spaces [W G, W2 A]. Generalizing the classical correspondence between isomorphism classes of central extensions of a group G by an abelian group A. We then prove an analogous theorem for central extensions of presheaves of simplicial groups. Finally, we use the correspondence to show that the cup product factors through a Heisenberg central extension.

ISBN: 9798684653056Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Simplicial groups

Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups.
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100 1 $a Niemeier, Michael. $0 (orcid)0000-0003-1011-3642 $3 3558909
245 1 0 $a Central Extensions of Simplicial Groups Protect and Presheaves of Simplicial Groups.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 100 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Aldrovandi, Ettore.
502 $a Thesis (Ph.D.)--The Florida State University, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a We show that path components of central extensions of a simplicial group G by a simplicial abelian group A are in bijection with the homotopy classes of maps between classifying spaces [W G, W2 A]. Generalizing the classical correspondence between isomorphism classes of central extensions of a group G by an abelian group A. We then prove an analogous theorem for central extensions of presheaves of simplicial groups. Finally, we use the correspondence to show that the cup product factors through a Heisenberg central extension.
590 $a School code: 0071.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Simplicial groups
653 $a Homotopy classes of maps
653 $a Heisenberg central extension
690 $a 0405
690 $a 0642
710 2 $a The Florida State University. $b Mathematics. $3 2095897
773 0 $t Dissertations Abstracts International $g 82-05B.
790 $a 0071
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27995537