1. CJM 2013 (vol 65 pp. 843)
 Jonsson, Jakob

3torsion in the Homology of Complexes of Graphs of Bounded Degree
For $\delta \ge 1$ and $n \ge 1$, consider the simplicial
complex of graphs on $n$ vertices in which each vertex has degree
at most $\delta$; we identify a given graph with its edge set and
admit one loop at each vertex.
This complex is of some importance in the theory of semigroup
algebras.
When $\delta = 1$, we obtain the
matching complex, for which it is known that
there is $3$torsion in degree $d$ of the homology
whenever $\frac{n4}{3} \le d \le \frac{n6}{2}$.
This paper establishes similar bounds for $\delta \ge
2$. Specifically, there is $3$torsion in degree $d$ whenever
$\frac{(3\delta1)n8}{6} \le d \le \frac{\delta (n1) 
4}{2}$.
The procedure for detecting
torsion is to construct an explicit cycle $z$ that is easily seen
to have the property that $3z$ is a boundary. Defining a
homomorphism that sends
$z$ to a nonboundary element in the chain complex of a certain
matching complex, we obtain that $z$ itself is a nonboundary.
In particular, the homology class of $z$ has order $3$.
Keywords:simplicial complex, simplicial homology, torsion group, vertex degree Categories:05E45, 55U10, 05C07, 20K10 

2. CJM 2001 (vol 53 pp. 780)
 Nicolaescu, Liviu I.

SeibergWitten Invariants of Lens Spaces
We show that the SeibergWitten invariants of a lens space determine
and are determined by its CassonWalker invariant and its
ReidemeisterTuraev torsion.
Keywords:lens spaces, Seifert manifolds, SeibergWitten invariants, CassonWalker invariant, Reidemeister torsion, eta invariants, DedekindRademacher sums Categories:58D27, 57Q10, 57R15, 57R19, 53C20, 53C25 

3. CJM 2000 (vol 52 pp. 695)
 Carey, A.; Farber, M.; Mathai, V.

Correspondences, von Neumann Algebras and Holomorphic $L^2$ Torsion
Given a holomorphic Hilbertian bundle on a compact complex manifold, we
introduce the notion of holomorphic $L^2$ torsion, which lies in the
determinant line of the twisted $L^2$ Dolbeault cohomology and
represents a volume element there. Here we utilise the theory of
determinant lines of Hilbertian modules over finite von~Neumann
algebras as developed in \cite{CFM}. This specialises to the
RaySingerQuillen holomorphic torsion in the finite dimensional case.
We compute a metric variation formula for the holomorphic $L^2$
torsion, which shows that it is {\it not\/} in general independent of
the choice of Hermitian metrics on the complex manifold and on the
holomorphic Hilbertian bundle, which are needed to define it. We
therefore initiate the theory of correspondences of determinant lines,
that enables us to define a relative holomorphic $L^2$ torsion for a
pair of flat Hilbertian bundles, which we prove is independent of the
choice of Hermitian metrics on the complex manifold and on the flat
Hilbertian bundles.
Keywords:holomorphic $L^2$ torsion, correspondences, local index theorem, almost KÃ¤hler manifolds, von~Neumann algebras, determinant lines Categories:58J52, 58J35, 58J20 
