Higher Franz-Reidemeister torsion

By Kiyoshi Igusa. 2002

121 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/741b44fe4a3de1dea05a46a9d088c6e0a71904e7

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Triangulated surfaces in triangulated categories (2013, background): “, [Igu02]), that we have a weak equivalence of topological spaces ∣N(Rib3)∣ ≃ ∐ (S,M) BG(S,M)”
Cohomological structure of the mapping class group and beyond (2005, methodology): “rmined by Borel [6][7]. In the case of OutFn, Igusa proved the following remarkable result which shows a sharp contrast with the case of the mapping class group (see Theorem 8.5.3 and Remark 8.5.4 of [38]). Theorem 8 (Igusa[38]). The homomorphism Hek(GL(n,Z);Q)−→Hek(OutF n;Q) induced by the natural ”
Metrics of positive scalar curvature and generalised Morse functions, part I (2008, methodology): “ work for compact families of admissible Morse functions is a more delicate matter. The ﬁrst problem is to deﬁne what we mean by a “family”. We employ the notion described by Igusa in chapter four of [16] where a family is a certain bundle of ﬁbrewise Morse functions. We will review this in more det”
COHOMOLOGICAL ASPECTS OF MAGNUS EXPANSIONS. (2005, methodology): “her hand, as was established by Culler and Vogtmann [CV], the virtual cohomology dimension of Aut(Fn) is 2n−2. Hence, if m≥2n−1, then Hm(Aut(Fn);Q) = 0. This completes the proof of the theorem. Igusa [I], Theorem 8.5.3, p.333, proved the homomorphism of reduced cohomology He∗(GL(H Z);Q) →He∗(Aut(Fn)”
A bordism approach to string topology (2003, unknown): “2864 David Chataur Let us describe these categorical constructions (see [6, 20]).”
Automorphism groups of free groups, surface groups and free abelian groups (2005, background): “However, a result of Igusa’s [47] shows that this does not work for GL(n,Z): the map from Out(Fn) to GL(n,Z) is trivial on homology in the stable range.”