26. CMB 2010 (vol 54 pp. 147)
 Nelson, Sam

Generalized Quandle Polynomials
We define a family of generalizations of the twovariable quandle polynomial.
These polynomial invariants generalize in a natural way to eightvariable
polynomial invariants of finite biquandles. We use these polynomials to define
a family of link invariants that further generalize the quandle counting
invariant.
Keywords:finite quandles, finite biquandles, link invariants Categories:57M27, 76D99 

27. CMB 2010 (vol 53 pp. 706)
28. CMB 2010 (vol 53 pp. 542)
29. CMB 2009 (vol 52 pp. 257)
 Ikeda, Toru

Essential Surfaces in Graph Link Exteriors
An irreducible graph manifold $M$ contains an essential torus if
it is not a special Seifert manifold.
Whether $M$ contains a closed essential surface of
negative Euler characteristic or not
depends on the difference of Seifert fibrations from the two sides
of a torus system which splits $M$ into Seifert manifolds.
However,
it is not easy to characterize geometrically the class of
irreducible graph manifolds which contain such surfaces.
This article studies this problem in the case of graph link exteriors.
Keywords:Graph link, Graph manifold, Seifert manifold, Essential surface Category:57M25 

30. CMB 2008 (vol 51 pp. 508)
 Cavicchioli, Alberto; Spaggiari, Fulvia

A Result in Surgery Theory
We study the topological $4$dimensional surgery problem
for a closed connected orientable
topological $4$manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.
Keywords:fourmanifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map Categories:57N65, 57R67, 57Q10 

31. CMB 2008 (vol 51 pp. 535)
32. CMB 2007 (vol 50 pp. 481)
 Blanlœil, Vincent; Saeki, Osamu

Concordance des nÅuds de dimension $4$
We prove that for a simply connected closed
$4$dimensional manifold, its embeddings
into the sphere of dimension $6$ are all
concordant to each other.
Keywords:concordance, cobordisme, n{\oe}ud de dimension $4$, chirurgie plongÃ©e Categories:57Q45, 57Q60, 57R40, 57R65, 57N13 

33. CMB 2007 (vol 50 pp. 365)
 Godinho, Leonor

Equivariant Cohomology of $S^{1}$Actions on $4$Manifolds
Let $M$ be a symplectic $4$dimensional manifold equipped with a
Hamiltonian circle action with isolated fixed points. We describe a
method for computing its integral equivariant cohomology in terms of
fixed point data. We give some examples of these computations.
Categories:53D20, 55N91, 57S15 

34. CMB 2007 (vol 50 pp. 390)
35. CMB 2007 (vol 50 pp. 206)
 Golasiński, Marek; Gonçalves, Daciberg Lima

Spherical Space Forms: Homotopy Types and SelfEquivalences for the Group $({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times SL_2\,(\mathbb{F}_p)$
Let $G=({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times
\SL_2(\mathbb{F}_p)$, and let $X(n)$ be an $n$dimensional
$CW$complex of the homotopy type of an $n$sphere. We study the
automorphism group $\Aut (G)$ in order to compute the number of
distinct homotopy types of spherical space forms with respect to free
and cellular $G$actions on all $CW$complexes $X(2dn1)$, where $2d$
is the period of $G$. The groups ${\mathcal E}(X(2dn1)/\mu)$ of self
homotopy equivalences of space forms $X(2dn1)/\mu$ associated with
free and cellular $G$actions $\mu$ on $X(2dn1)$ are determined as
well.
Keywords:automorphism group, $CW$complex, free and cellular $G$action, group of self homotopy equivalences, LyndonHochschildSerre spectral sequence, special (linear) group, spherical space form Categories:55M35, 55P15, 20E22, 20F28, 57S17 

36. CMB 2006 (vol 49 pp. 624)
 Teragaito, Masakazu

On NonIntegral Dehn Surgeries Creating NonOrientable Surfaces
For a nontrivial knot in the $3$sphere,
only integral Dehn surgery can create a closed $3$manifold containing a projective plane.
If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true.
In contrast to these, we show that nonintegral surgery on a hyperbolic knot
can create a closed nonorientable surface of any genus greater than two.
Keywords:knot, Dehn surgery, nonorientable surface Category:57M25 

37. CMB 2006 (vol 49 pp. 337)
 Berlanga, R.

Homotopy Equivalence and Groups of MeasurePreserving Homeomorphisms
It is shown that the group of compactly
supported, measurepreserving homeomorphisms of a
connected, second countable manifold is locally contractible in the direct limit topology.
Furthermore, this group is weakly homotopically equivalent to the more general group of
compactly supported homeomorphisms.
Categories:57S05, 58F11 

38. CMB 2006 (vol 49 pp. 55)
 Dubois, Jérôme

Non Abelian Twisted Reidemeister Torsion for Fibered Knots
In this article, we give an explicit formula to compute the
non abelian twisted signdeter\mined Reidemeister torsion of the
exterior of a fibered knot in terms of its monodromy. As an
application, we give explicit formulae for the non abelian
Reidemeister torsion of torus knots and of the figure eight knot.
Keywords:Reidemeister torsion, Fibered knots, Knot groups, Representation space, $\SU$, $\SL$, Adjoint representation, Monodromy Categories:57Q10, 57M27, 57M25 

39. CMB 2006 (vol 49 pp. 36)
40. CMB 2005 (vol 48 pp. 547)
 Fehér, L. M.; Némethi, A.; Rimányi, R.

Degeneracy of 2Forms and 3Forms
We study some global aspects of differential complex 2forms and 3forms
on complex manifolds.
We compute the cohomology classes represented by the sets of points
on a manifold where such a form degenerates in various senses,
together with other similar cohomological obstructions.
Based on these results and a formula for projective
representations, we calculate the degree of the projectivization
of certain orbits of the representation $\Lambda^k\C^n$.
Keywords:Classes of degeneracy loci, 2forms, 3forms, Thom polynomials, global singularity theory Categories:14N10, 57R45 

41. CMB 2005 (vol 48 pp. 32)
 Dąbkowski, Mieczysław K.; Przytycki, Józef H.; Togha, Amir A.

NonLeftOrderable 3Manifold Groups
We show that several torsion free 3manifold groups
are not leftorderable.
Our examples are groups of cyclic branched coverings of $S^3$
branched along links.
The figure eight knot provides simple
nontrivial examples. The groups arising in these examples are known
as Fibonacci groups which we show not to be leftorderable.
Many other examples of nonorderable groups are obtained by taking
3fold branched covers of $S^3$ branched along various hyperbolic
2bridge knots.
%with various hyperbolic 2bridge knots as branched sets.
The manifold obtained in such a way from the $5_2$ knot
is of special interest as it is conjectured to be the hyperbolic
3manifold with the smallest volume.
Categories:57M25, 57M12, 20F60 

42. CMB 2004 (vol 47 pp. 332)
 Charette, Virginie; Goldman, William M.; Jones, Catherine A.

Recurrent Geodesics in Flat Lorentz $3$Manifolds
Let $M$ be a complete flat Lorentz $3$manifold $M$ with purely
hyperbolic holonomy $\Gamma$. Recurrent geodesic rays are completely
classified when $\Gamma$ is cyclic. This implies that for any pair of
periodic geodesics $\gamma_1$, $\gamma_2$, a unique geodesic forward
spirals towards $\gamma_1$ and backward spirals towards $\gamma_2$.
Keywords:geometric structures on lowdimensional manifolds, notions of recurrence Categories:57M50, 37B20 

43. CMB 2004 (vol 47 pp. 439)
 Parker, John R.

On the Stable Basin Theorem
The stable basin theorem was introduced by Basmajian and Miner as a
key step in their necessary condition for the discreteness of a
nonelementary group of complex hyperbolic isometries. In this
paper we improve several of Basmajian and Miner's key estimates and
so give a substantial improvement on the main inequality in the
stable basin theorem.
Categories:22E40, 20H10, 57S30 

44. CMB 2004 (vol 47 pp. 60)
 Little, Robert D.

Rational Integer Invariants of Regular Cyclic Actions
Let $g\colon M^{2n}\rightarrow M^{2n}$ be a smooth map of period $m>2$ which
preserves orientation. Suppose that the cyclic action defined by $g$ is regular
and that the normal bundle of the fixed point set $F$ has a $g$equivariant
complex structure. Let $F\pitchfork F$ be the transverse selfintersection of
$F$ with itself. If the $g$signature $\Sign (g,M)$ is a rational integer and
$n<\phi (m)$, then there exists a choice of orientations such that $\Sign(g,M)=
\Sign F=\Sign(F\pitchfork F)$.
Category:57S17 

45. CMB 2003 (vol 46 pp. 617)
 Pak, Hong Kyung

On Harmonic Theory in Flows
Recently [8], a harmonic theory was developed for a compact
contact manifold from the viewpoint of the transversal geometry of
contact flow. A contact flow is a typical example of geodesible
flow. As a natural generalization of the contact flow, the present
paper develops a harmonic theory for various flows on compact
manifolds. We introduce the notions of $H$harmonic and
$H^*$harmonic spaces associated to a H\"ormander flow. We also
introduce the notions of basic harmonic spaces associated to a weak
basic flow. One of our main results is to show that in the special
case of isometric flow these harmonic spaces are isomorphic to the
cohomology spaces of certain complexes. Moreover, we find an
obstruction for a geodesible flow to be isometric.
Keywords:contact structure, geodesible flow, isometric flow, basic cohomology Categories:53C20, 57R30 

46. CMB 2003 (vol 46 pp. 356)
47. CMB 2003 (vol 46 pp. 310)
48. CMB 2003 (vol 46 pp. 265)
 Oh, Seungsang

Reducing Spheres and Klein Bottles after Dehn Fillings
Let $M$ be a compact, connected, orientable, irreducible 3manifold with a
torus boundary. It is known that if two Dehn fillings on $M$ along the
boundary produce a reducible manifold and a manifold containing a Klein
bottle, then the distance between the filling slopes is at most three. This
paper gives a remarkably short proof of this result.
Keywords:Dehn filling, reducible, Klein bottle Category:57M50 

49. CMB 2003 (vol 46 pp. 122)
 Moon, Myoungho

On Certain Finitely Generated Subgroups of Groups Which Split
Define a group $G$ to be in the class $\mathcal{S}$ if for any
finitely generated subgroup $K$ of $G$ having the property that
there is a positive integer $n$ such that $g^n \in K$ for all
$g\in G$, $K$ has finite index in $G$. We show that a free
product with amalgamation $A*_C B$ and an $\HNN$ group $A *_C$ belong
to $\mathcal{S}$, if $C$ is in $\mathcal{S}$ and every subgroup of
$C$ is finitely generated.
Keywords:free product with amalgamation, $\HNN$ group, graph of groups, fundamental group Categories:20E06, 20E08, 57M07 

50. CMB 2002 (vol 45 pp. 231)
 Hironaka, Eriko

Erratum:~~The Lehmer Polynomial and Pretzel Links
Erratum to {\it The Lehmer Polynomial and Pretzel Links},
Canad. J. Math. {\bf 44}(2001), 440451.
Keywords:Alexander polynomial, pretzel knot, Mahler measure, Salem number, Coxeter groups Categories:57M05, 57M25, 11R04, 11R27 
