scholarly journals Geometric recursion from polytope triangulations and twisted homology

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Twisted Homology

scholarly journals Profinite rigidity for twisted Alexander polynomials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jun Ueki
Keyword(s):  
Rigidity Theorem ◽  
Homology Groups ◽  
Alexander Polynomials ◽  
Twisted Homology ◽  
Hyperbolic Volumes

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.

scholarly journals Twisted Homology of Quantum SL(2) - Part II

2009 ◽  
Vol 6 (1) ◽  
pp. 69-98 ◽  
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.

scholarly journals Twisted Homology of Quantum SL(2)

K-Theory ◽  
2005 ◽  
Vol 34 (4) ◽  
pp. 327-360 ◽  
Author(s):  
Tom Hadfield ◽  
Ulrich Krähmer
Keyword(s):  
Twisted Homology

scholarly journals Twisted simplicial groups and twisted homology of categories

2017 ◽  
Vol 19 (2) ◽  
pp. 111-130
Author(s):  
J. Y. Li ◽  
V. V. Vershinin ◽  
J. Wu
Keyword(s):  
Twisted Homology

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

What's Next? ◽  
2020 ◽  
pp. 1-20
Author(s):  
Ian Agol ◽  
Nathan M. Dunfield
Keyword(s):  
Thurston Norm ◽  
Twisted Homology

Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of S-integers

2018 ◽  
Vol 27 (05) ◽  
pp. 1850033 ◽  
Author(s):  
Ryoto Tange
Keyword(s):  
Number Field ◽  
Asymptotic Growth ◽  
Homology Groups ◽  
Finite Set ◽  
Twisted Homology ◽  
Alexander Invariants

We present a generalization of the Fox formula for twisted Alexander invariants associated to representations of knot groups over rings of [Formula: see text]-integers of [Formula: see text], where [Formula: see text] is a finite set of finite primes of a number field [Formula: see text]. As an application, we give the asymptotic growth of twisted homology groups.

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