We prove that the primitive elements of the first homology group of a genus g torus can be represented by a simple closed curve.Let T be a closed orientable surface with g handles (g > 0). The first homology group, HX(T), is the free abelian group on 2g generators. In general, if an element of Hx (T) is represented by a closed curve, the curve must cross itself. However, we prove that if the element is primitive, then it can be represented by a simple closed curve. Primitive means not divisible by an integer greater than one. Our proof is accomplished through use of the "twist" homeomorphism described by Lickorish [1].Let ak and Bk be the standard oriented simple closed curves around the kth handle of T for 1 < k < g. So each a, or /?■ represents a basis element of Hx (T). For 1 < k < g, let yk be a simple closed curve looping the kth and (A: + l)st handles of T. The Lickorish "twist" homeomorphism about a simple closed curve J is defined by cutting T along J, giving a full twist to one edge, and then gluing T back together along J. Twists about ak, Bk, and yk induce automorphisms on HX(T) carrying {■ ■ ■ ,

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In 1970 Roger Fenn showed that one could always balance a square table on a hill. Soon after, Joseph Zaks stated that one can always translate a triangular chair to balance on a hill. Recent results have been found by E. H. Kronheimer and P. B. Kronheimer. This paper gives precise statements of the theorems and shows that:1. Compact support for the hill in the Chair Theorem cannot be replaced by lim| x |_oo/(x) = 0 (answering a question of Zaks). The isometry of theTable cannot be replaced by a translation. 3. The square Table cannot be replaced by an n-gon table for n > 5. 4. The Table Theorem is still open for cyclic quadrilaterals.

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