On the normal cycles of subanalytic sets

We present a short complete proof of the existence of the normal cycle of a compact subanalytic set. The approach is inspired by some old ides of Joseph Fu, uses Morse theoretic techniques and $o$-minimal topology.Comment: 24 pages, 1 figure. Vers 4: filled in some missing details, included an approximation result, a comparison with the approach of A. Bernig and a several appendice

On the Reidemeister torsion of rational homology spheres

We prove that the mod Z reduction of the torsion of a rational homology 3-sphere is completely determined by three data: a certain canonical spin^c structure, the linking form and a Q/Z-valued constant c. This constant is a new topological invariant of the rational homology sphere. Experimentations with lens spaces suggest this constant may be as powerful an invariant as the torsion itself.Comment: 6 page