  We study the construction and properties of the Gysin triangle in an
axiomatic framework which covers triangulated mixed motives and MGl-modules
over an arbitrary base S. This allows to define the Gysin morphism associated
to a projective morphism between smooth S-schemes and prove duality for
projective smooth S-schemes. As part of the construction, cobordism classes are
considered and we give a proof of the Myschenko theorem generalized in our
context - this in fact gives another proof of the latter theorem in classical
stable homotopy through complex realization. Finally, these constructions apply
to rigid cohomology through the notion of a mixed Weil theory introduced by
D.-C. Cisinski and the author in another work.

Algebraic Geometry;Algebraic Topology