Introduction to Combinatorial Torsions

By Vladimir Turaev. 2001

286 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8439a0d795dc7bf41c77b6c34e4e0b2d77270b38

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Citations in the corpus

Higher‐dimensional Reidemeister torsion invariants for cusped hyperbolic 3‐manifolds (2011, background): “By the behaviour of the torsion under change of bases in homology [22, 31], Proposition 4.”
Twisted Alexander polynomials detect fibered 3-manifolds (2008, background): “Furthermore it follows from Fact 3, [ Tu01 , Theorem 3.4] and [Tu01,”
The Thurston norm, fibered manifolds and twisted Alexander polynomials (2005, methodology): “We need the following theorem which can be found in [26].”
The decategorification of sutured Floer homology (2009, background): “l) ∈F to be the torsion of the based acyclic complex C ∗(X,Y;F). It is straightforward to check that this is independent of the choice of representative lift corresponding to l ∈Lift(X,Y).We refer to [Tu01] for an excellent introduction to the torsion of based complexes. The torsion τϕ(X,Y,l) ∈F is ”
Simplicial matrix-tree theorems (2008, unknown): “, [35].”
The Thurston norm and twisted Alexander polynomials (2012, background): “}. Note that φinduces a homomorphism C[F]S−1 → C(t) which we also denote by φ. The following is a slight generalization of [FK08, Theorem 6.6], which in turn builds on ideas of Turaev (cf. [Tu86] and [Tu01]). Proposition 3.3. We have τ(N,α) ∈ C[F]S−1, and τ(N,φ,α) . = φ(τ(N,α)). 6 STEFANFRIEDLANDSTE”
A SURVEY OF TWISTED ALEXANDER POLYNOMIALS (2009, methodology): “0 ∆α N,i (−1)i+1 . The following is a mild extension of [FK06, Proposition 2.5], [FK08a, Lemmas 6.2 and 6.3] and [FK08a, Theorem 6.7]. Most of the ideas go back to work of Turaev (cf. e.g. [Tu86] and [Tu01]). Proposition 3.2. Let N be a 3–manifold with empty or toroidal boundary, ψ: π1(N) → F a non–”