51. CMB 1999 (vol 42 pp. 248)
 Weber, Christian

The Classification of $\Pin_4$Bundles over a $4$Complex
In this paper we show that the Liegroup $\Pin_4$ is isomorphic to
the semidirect product $(\SU_2\times \SU_2)\timesv \Z/2$ where
$\Z/2$ operates by flipping the factors. Using this structure
theorem we prove a classification theorem for $\Pin_4$bundles over
a finite $4$complex $X$.
Categories:55N25, 55R10, 57S15 

52. CMB 1999 (vol 42 pp. 149)
 Boyer, S.; Zhang, X.

A Note on Finite Dehn Fillings
Let $M$ be a compact, connected, orientable 3manifold whose
boundary is a torus and whose interior admits a complete hyperbolic
metric of finite volume. In this paper we show that if the minimal
CullerShalen norm of a nonzero class in $H_1(\partial M)$ is
larger than $8$, then the finite surgery conjecture holds for $M$.
This means that there are at most $5$ Dehn fillings of $M$ which
can yield manifolds having cyclic or finite fundamental groups and
the distance between any slopes yielding such manifolds is at most
$3$.
Categories:57M25, 57R65 

53. CMB 1999 (vol 42 pp. 46)
 Dijkstra, Jan J.

Generic Partial TwoPoint Sets Are Extendable
It is shown that under $\ZFC$ almost all planar compacta that meet
every line in at most two points are subsets of sets that meet every
line in exactly two points. This result was previously obtained by the
author jointly with K.~Kunen and J.~van~Mill under the assumption that
Martin's Axiom is valid.
Category:57N05 

54. CMB 1999 (vol 42 pp. 52)
 Edmonds, Allan L.

Embedding Coverings in Bundles
If $V\to X$ is a vector bundle of fiber dimension $k$ and $Y\to X$
is a finite sheeted covering map of degree $d$, the implications
for the Euler class $e(V)$ in $H^k(X)$ of $V$ implied by the
existence of an embedding $Y\to V$ lifting the covering map are
explored. In particular it is proved that $dd'e(V)=0$ where $d'$
is a certain divisor of $d1$, and often $d'=1$.
Categories:57M10, 55R25, 55S40, 57N35 

55. CMB 1998 (vol 41 pp. 374)
 Young, Carmen M.

Normal invariants of lens spaces
We show that normal and stable normal invariants of polarized
homotopy equivalences of lens spaces $M = L(2^m;\r)$ and
$N = L(2^m;\s)$ are determined by certain $\ell$polynomials
evaluated on the elementary symmetric functions
$\sigma_i(\rsquare)$ and $\sigma_i(\ssquare)$. Each polynomial
$\ell_k$ appears as the homogeneous part of degree $k$ in the
Hirzebruch multiplicative $L$sequence. When $n = 8$, the
elementary symmetric functions alone determine the relevant normal
invariants.
Categories:57R65, 57S25 

56. CMB 1998 (vol 41 pp. 252)
57. CMB 1998 (vol 41 pp. 140)
58. CMB 1997 (vol 40 pp. 309)
 Hillman, J. A.; Sakuma, M.

On the homology of finite abelian coverings of links
Let $A$ be a finite abelian group and $M$ be a
branched cover of an homology $3$sphere, branched over a link $L$,
with covering group $A$. We show that $H_1(M;Z[1/A])$ is determined
as a $Z[1/A][A]$module by the Alexander ideals of $L$ and certain
ideal class invariants.
Keywords:Alexander ideal, branched covering, Dedekind domain,, knot, link. Category:57M25 

59. CMB 1997 (vol 40 pp. 370)
 Rolfsen, Dale; Zhongmou, Li

Which $3$manifolds embed in $\Triod \times I \times I$?
We classify the compact $3$manifolds whose boundary is a union of
$2$spheres, and which embed in $T \times I \times I$, where $T$ is a
triod and $I$ the unit interval. This class is described explicitly as
the set of punctured handlebodies. We also show that any $3$manifold
in $T \times I \times I$ embeds in a punctured handlebody.
Categories:57N10, 57N35, 57Q35 

60. CMB 1997 (vol 40 pp. 204)