  The Atiyah-Singer index theorem gives a topological formula for the index of
an elliptic differential operator. Enlightening from Alain Connes' tangent
groupoid proof of the index theorem and van Erp's research for the Heisenberg
index theory on contact manifolds, we give an explicit construction of a series
of maps, whose induced map in K-theory is the Heisenberg Atiyah-Singer index
map on contact manifolds. Our methods derive from Higson's construction for
symbol class in K-theory.
