Expand all Collapse all | Results 51 - 57 of 57 |
51. CMB 1999 (vol 42 pp. 52)
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 $d-1$, and often $d'=1$.
Categories:57M10, 55R25, 55S40, 57N35 |
52. CMB 1998 (vol 41 pp. 374)
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 |
53. CMB 1998 (vol 41 pp. 252)
Dihedral groups of automorphisms of compact Riemann surfaces In this note we determine which dihedral subgroups of $\GL_g(\D C)$ can
be realized by group actions on Riemann surfaces of genus $g>1$.
Category:57H20 |
54. CMB 1998 (vol 41 pp. 140)
Skein homology A new class of homology groups associated to a 3-manifold is defined.
The theories measure the syzygies between skein relations in a skein
module. We investigate some of the properties of the homology theory
associated to the Kauffman bracket.
Categories:57M25, 57M99 |
55. CMB 1997 (vol 40 pp. 309)
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 |
56. CMB 1997 (vol 40 pp. 370)
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 |
57. CMB 1997 (vol 40 pp. 204)
The $\eta$-invariants of cusped hyperbolic $3$-manifolds In this paper, we define the $\eta$-invariant for a cusped hyperbolic
$3$-manifold and discuss some of its applications. Such an
invariant detects the chirality of a hyperbolic knot or link and
can be used to distinguish many links with homeomorphic complements.
Categories:57M50, 53C30, 58G25 |