paper ” Floating bundles and their applications ”

Supplement 2 to the paper " Floating bundles and their applications " A.V. Ershov This paper is the supplement to the section 2 of the paper " Floating bundles and their applications " [1]. Below we study some properties of category, connected with cobordism rings of FBSP. In particular, we shall show that it is the tensor category. In [1] the series G(x, y) ∈ H[[x, y]] = Ω * U (Gr), where H = Ω * U (Gr), was defined. Recall that it corresponds to the direct limit κ of the maps κ k,l : Gr k,kl → CP kl−1 , where Gr k,kl is the canonical FBSP over Gr k,kl ((k, l) = 1). In [1] some properties of G(x, y) were studied. In particular, it was shown that (εG)(x, y) = F (x, y), (pt) is the counit of the Hopf algebra H and F (x, y) ∈ R[[x, y]] is the formal group of geometric cobordisms.