We define invariants < L)−1 and FL(A) for links L in Σ × R where Σ is a surface by using the idea of Kauffman bracket. We compute < L)−1 in case of Σ = P2, a projective plane. In case of Σ = T2, a torus, we show examples of computations of FL(A) for a certain class of links L in T2 × R related to genus 1 Heegaard diagrams of lens spaces and a relation among them. This relation implies that FL(A) is a topological invariant for lens spaces in a certain sense.