Certifying the Thurston Norm via SL(2,C)-twisted Homology

AbstractWe formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a {{\mathbb{Z}}}-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

Download Full-text

The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm

What's Next? ◽

10.1515/9780691185897-003 ◽

2019 ◽

pp. 21-44

Keyword(s):

Profinite Completion ◽

Thurston Norm

Download Full-text

Intersection Numbers for Twisted Homology

manuscripta mathematica ◽

10.1007/s00229-004-0454-0 ◽

2004 ◽

Vol 114 (2) ◽

Author(s):

Toyoshi Togi

Keyword(s):

Intersection Numbers ◽

Twisted Homology

Download Full-text

Twisted Homology of Quantum SL(2) - Part II

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is009009022jkt091 ◽

2009 ◽

Vol 6 (1) ◽

pp. 69-98 ◽

Cited By ~ 5

Author(s):

Tom Hadfield ◽

Ulrich Krähmer

Keyword(s):

Noncommutative Geometry ◽

Hochschild Cohomology ◽

Cyclic Homology ◽

Coordinate Ring ◽

Volume Form ◽

Twisted Homology

AbstractWe complete the calculation of the twisted cyclic homology of the quantised coordinate ring = ℂq [SL(2)] of SL(2) that we began in [14]. In particular, a nontrivial cyclic 3-cocycle is constructed which also has a nontrivial class in Hochschild cohomology and thus should be viewed as a noncommutative geometry analogue of a volume form.

Download Full-text