"Endomorphisms of the Lie Algebroids TM×g up to Homotopy"

(joint work with B.Balcerzak and W.Walas, Universitatis Iagellonicae Acta Mathematica, 2002 (in print))
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The notion of a homotopy joining two homomorphisms of Lie algebroids comes from J.Kubarski and the definition of the fundamental group p(A) of a Lie algebroid A (which consists of homotopy classes of strong automorphisms of A, from B.Balcerzak. It is given in this paper a homotopic classification of strong homomorphisms of the trivial Lie algebroid TM×g and computed the fundamental group of the algebroid TM×R with the aid of H¹_dR(M).