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An Algebraic Characterization of the...

The University of Chicago.

An Algebraic Characterization of the Point-Pushing Subgroup.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	An Algebraic Characterization of the Point-Pushing Subgroup./
Author:	Akin, Victoria Suzanne.
Description:	1 online resource (57 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355076110

An Algebraic Characterization of the Point-Pushing Subgroup.
Akin, Victoria Suzanne.

An Algebraic Characterization of the Point-Pushing Subgroup. - 1 online resource (57 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

The point-pushing subgroup, P(Sigmag) of the mapping class group Mod(Sigmag,1) of a surface with marked point is an embedding of pi1(Sigma g) given by pushing the marked point around loops. We prove that for g≥ 3, the subgroup P (Sigmag) is the unique normal, genus g surface subgroup of Mod(Sigma g,1). As a corollary to this uniqueness result, we give a new proof that Out(Mod+/-(Sigma g,1)) = 1, where Out denotes the outer automorphism group; a proof which does not use automorphisms of complexes of curves. Ingredients in our proof of this characterization theorem include combinatorial group theory, representation theory, the Johnson theory of the Torelli group, surface topology, and the theory of Lie algebras.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355076110Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

An Algebraic Characterization of the Point-Pushing Subgroup.
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035 $a (MiAaPQ)uchicago:13697
035 $a AAI10264314
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Akin, Victoria Suzanne. $3 1180666
245 1 3 $a An Algebraic Characterization of the Point-Pushing Subgroup.
264 0 $c 2017
300 $a 1 online resource (57 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Benson Farb.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a The point-pushing subgroup, P(Sigmag) of the mapping class group Mod(Sigmag,1) of a surface with marked point is an embedding of pi1(Sigma g) given by pushing the marked point around loops. We prove that for g≥ 3, the subgroup P (Sigmag) is the unique normal, genus g surface subgroup of Mod(Sigma g,1). As a corollary to this uniqueness result, we give a new proof that Out(Mod+/-(Sigma g,1)) = 1, where Out denotes the outer automorphism group; a proof which does not use automorphisms of complexes of curves. Ingredients in our proof of this characterization theorem include combinatorial group theory, representation theory, the Johnson theory of the Torelli group, surface topology, and the theory of Lie algebras.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Chicago. $b Mathematics. $3 1180611
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10264314 $z click for full text (PQDT)

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