dc.contributor.authorSiejakowski, Rafał, M.
dc.identifier.citationSiejakowski, R. M. (2017). On the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifolds. Doctoral thesis, Nanyang Technological University, Singapore.
dc.description.abstractThe non-abelian Reidemeister torsion is a numerical invariant of cusped hyperbolic 3-manifolds defined by J. Porti (1997) in terms of the adjoint holonomy representation of the hyperbolic structure. We develop a geometric approach to the definition and computation of the torsion using infinitesimal isometries. For manifolds carrying positively oriented geometric ideal triangulations, we establish a fundamental relationship between the derivatives of Thurston's gluing equations and the cohomology of the sheaf of infinitesimal isometries. Using these results, we obtain a partial confirmation of the "1-loop Conjecture" of Dimofte and Garoufalidis (2013) which expresses the non-abelian torsion in terms of the combinatorics of the gluing equations. In this way, we reduce the Conjecture to a certain normalization property of the Reidemeister torsion of free groups.en_US
dc.format.extent123 p.en_US
dc.titleOn the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifoldsen_US
dc.contributor.supervisorAndrew James Krickeren_US
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.degree​Doctor of Philosophy (SPMS)en_US

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