  Let $A$ be a regular ring over a field $k$, with $1/2\in k$ and dimension
$d$. We discuss the Homotopy Conjecture of Madhav V. Nori, in the complete
intersection case (meaning when the projective module in question if free, of
rank at least 2). Recently, an obstruction set (sheaf) $\pi_0(Q_{2n})(A)$ was
introduced [F] to detect when a surjective map $A^n\to I/I^2$ lifts to a
surjective map $A^n\to I$. We establish that $\pi_0(Q_{2n})(A)$ coincides with
the obstruction set of equivalence classes, originally suggested by Nori. We
also establish that $\pi_0(Q_{2n})(A)$ has a natural groups structure, when
$2n\geq d+2$. Further, we establish that, when $2n\geq d+2$, there is a
surjective homomorphism $E^n(A) \to \pi_0(Q_{2n})(A) $, where $E^n(A)$ denotes
the Euler class group defined by Bhatwadekar and Sridharan [BS2]. This
homomorphism is an isomorphism, whenever triviality, in $\pi_0(Q_{2n})(A)$, of
an orientation $(I, \omega_I), guarantees that $omega_I$ lifts to a surjective
map $A^n\to I$. We also give a Quadratic version of Lindel's Theorem, on
extendibility of projective modules.
