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Title: On the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifolds
Authors: Siejakowski, Rafał, M.
Keywords: DRNTU::Science::Chemistry
Issue Date: 2017
Source: Siejakowski, R. M. (2017). On the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifolds. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: The 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.
DOI: 10.32657/10356/72448
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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