Torelli Actions and Smooth Structures on 4-manifolds

Title:
Torelli Actions and Smooth Structures on 4-manifolds
Authors:
Calcut, Jack S.
Abstract:
Artin presentations are discrete equivalents of planar open book decompositions of closed, orientable three manifolds. Artin presentations characterize the fundamental groups of closed, orientable three manifolds. An Artin presentation also determines a smooth, compact, simply conected four manifold that bounds the three dimensional open book. In this way, the study of three and four manifolds may be approached purely group theoretically. In the theory of Artin presentations, elements of the Torelli subgroup act on the topology and smooth structures of the three and four manifolds. We show that the Torelli action can preserve the continuous topological type of a four manifold while changing its smooth structure. This is a new, group theoretic method of altering the smooth structure on a four manifold.
Citation:
Calcut, Jack S.. 2008. "Torelli Actions and Smooth Structures on 4-manifolds." Journal Of Knot Theory And Its Ramifications 17(2): 171-190.
Publisher:
World Scientific Publishing
DATE ISSUED:
2008
Department:
Mathematics
Type:
article
PUBLISHED VERSION:
10.1142/S0218216508006075
PERMANENT LINK:
http://hdl.handle.net/11282/309231

Full metadata record

DC FieldValue Language
dc.contributor.authorCalcut, Jack S.en_US
dc.date.accessioned2013-12-23T16:05:14Z-
dc.date.available2013-12-23T16:05:14Z-
dc.date.issued2008en
dc.identifier.citationCalcut, Jack S.. 2008. "Torelli Actions and Smooth Structures on 4-manifolds." Journal Of Knot Theory And Its Ramifications 17(2): 171-190.en_US
dc.identifier.issn0218-2165en_US
dc.identifier.urihttp://hdl.handle.net/11282/309231-
dc.description.abstractArtin presentations are discrete equivalents of planar open book decompositions of closed, orientable three manifolds. Artin presentations characterize the fundamental groups of closed, orientable three manifolds. An Artin presentation also determines a smooth, compact, simply conected four manifold that bounds the three dimensional open book. In this way, the study of three and four manifolds may be approached purely group theoretically. In the theory of Artin presentations, elements of the Torelli subgroup act on the topology and smooth structures of the three and four manifolds. We show that the Torelli action can preserve the continuous topological type of a four manifold while changing its smooth structure. This is a new, group theoretic method of altering the smooth structure on a four manifold.en_US
dc.publisherWorld Scientific Publishingen_US
dc.identifier.doi10.1142/S0218216508006075-
dc.subject.departmentMathematicsen_US
dc.titleTorelli Actions and Smooth Structures on 4-manifoldsen_US
dc.typearticleen_US
dc.identifier.journalJournal Of Knot Theory And Its Ramificationsen_US
dc.identifier.volume17en_US
dc.identifier.issue2en_US
dc.identifier.startpage171en_US
All Items in The Five Colleges of Ohio Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.