Show simple item record

dc.contributor.advisor Putman, Andrew
dc.contributor.advisor Wolf, Michael
dc.creatorBregman, Corey Joseph
dc.date.accessioned 2017-08-01T18:47:12Z
dc.date.available 2017-08-01T18:47:12Z
dc.date.created 2017-05
dc.date.issued 2017-04-20
dc.date.submitted May 2017
dc.identifier.citation Bregman, Corey Joseph. "Automorphisms of nonpositively curved cube complexes, right-angled Artin groups and homology." (2017) Diss., Rice University. https://hdl.handle.net/1911/96119.
dc.identifier.urihttps://hdl.handle.net/1911/96119
dc.description.abstract Recently, the geometry of CAT(0) cube complexes featured prominently in Agol’s resolution of two longstanding conjectures of Thurston in low-dimensional topology: the virtually Haken and virtually fibered conjecture for hyperbolic 3-manifolds. A key step of the proof was to show that every hyperbolic 3-manifold group is virtually special, i.e. virtually the fundamental group of a special nonpositively curved (NPC) cube complex. In this thesis, we study algebraic properties of special groups as they relate to the geometry of special cube complexes. In the first part of the thesis, we introduce a positive integer-valued invariant of special cube complexes called the genus, and show that having genus one is equivalent to having free abelian fundamental group. As a corollary, we obtain a new proof of the fact that every special group is either abelian or surjects onto a non-abelian free group. In the second part of the thesis, we turn our attention to automorphisms of NPC cube complexes. We give a criterion on a special cube complex which implies that any automorphism acts non-trivially on first homology, and show that a non- trivial action on homology can always be achieved by passing to covers. We then apply the criterion to provide a new geometric proof that the Torelli subgroup for a right-angled Artin group is torsion-free.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectGeometric group theory
CAT(0) geometry
low-dimensional topology
dc.title Automorphisms of nonpositively curved cube complexes, right-angled Artin groups and homology
dc.date.updated 2017-08-01T18:47:12Z
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record