
TL;DR
This paper extends the computation of algebraic and geometric invariants of torus bundles over lens spaces to all actions of a prime order group on lattices, including cases with non-discrete singular sets.
Contribution
It generalizes previous results by computing $L$-groups and structure sets for all $ ho:bZ/p o ext{GL}_n(bZ)$ actions, even with non-trivial fixed points.
Findings
Computed $L$-groups $L^{raket{j}}_m(bZ[bZ^n times_ ho bZ/p])$ for all actions.
Determined structure sets $bS^{geo,s}(M)$ in cases with non-discrete singular sets.
Extended previous work to more general group actions on lattices.
Abstract
Let be an odd prime and let be an action of on a lattice and let be the corresponding semidirect product. The torus bundle over the lens space has fundamental group . When fixes only the origin of , Davis and L\"uck \cite{DavisLuckTorusBundles} compute the -groups and the structure set . In this paper, we extend these computations to all actions of on . In particular, we compute and in a case where has a non-discrete singular set.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry
