316 research outputs found
Sections of surface bundles
A bundle with base and fibre aspherical closed surfaces has a section
if and only if the action factors through
and a cohomology class is 0. We simplify and make more explicit
the latter condition. We also show that the transgression in the
homology LHS spectral sequence of a central extension is evaluation of the
extension class. Examples with hyperbolic fibre and no section (based on ideas
of Endo) added.Comment: Some new background material. Section on flat fibred case rewritten.
In v3, details of Endo's example corrected and commentary added to final
section on question
On Farber's invariants for simple -knots
Let be a simple -knot with exterior . We show directly how the
Farber quintuple determines the homotopy type of
if the torsion subgroup of has odd order. We comment briefly on
the possible role of the EHP sequence in recovering the boundary inclusion from
the duality pairings and . Finally we reformulate the Farber
quintuple as an hermitian self-duality of an object in an additive category
with involution.Comment: v2. Minor reorganization and corrections to final sectio
An indecomposable PD_3-complex : II
We show that there are two homotopy types of PD_3-complexes with fundamental
group S_3*_{Z/2Z}S_3, and give explicit constructions for each, which differ
only in the attachment of the top cell.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-47.abs.htm
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