ON BOTT POLYNOMIALS

R. Bott defined two combinatorial invariants for finite cell complexes in the 1950's [2]. As described in [3], they fit beautifully into a state model framework. Recently, it has been observed that for finite graphs, the coefficients of this polynomial are the same set of invariants as defined by H. Whitney in [5]. In section 1, we define the Bott-Whitney polynomial and prove some of its basic properties. In section 2, we show that for a planar connected graph, the Bott-Whitney polynomial is essentially the chromatic polynomial of its dual graph. In section 3, an interpretation of the coefficients of the Bott-Whitney polynomial is given following Whitney [5]. In section 4, we study more general Bott polynomials.