Expand all Collapse all | Results 51 - 58 of 58 |
51. CMB 1999 (vol 42 pp. 46)
Generic Partial Two-Point 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 |
52. 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 |
53. 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 |
54. 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 |
55. 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 |
56. 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 |
57. 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 |
58. 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 |