The Simple Connectedness of a Tame Weakly Shod Algebra.

We prove that a tame weakly shod algebra A which is not quasi-tilted is simply connected if and only if the orbit graph of its pip-bounded component is a tree. or if and only if its first Hochschild cohomology group H²(A) with coefficients in AAA vanishes. We also show that it is strongly simply connected if and only if the orbit graph of each of its directed components is a tree, or if and only if H¹ (A) = 0 and it contains no full convex subcategory which is hereditary of type A. or if and only lilt is separated and contains no full convex subcategory which is hereditary of type A. [ABSTRACT FROM AUTHOR]