Abstract:
Given a compact manifold X, the set of simple manifold structures on X x \Delta^k relative to the boundary can be viewed as the k-th homotopy group of a space \S^s (X). This space is called the block structure space of X. We study the block structure spaces of real projective spaces. Generalizing Wall's join construction we show that there is a functor from the category of finite dimensional real vector spaces with inner product to the category of pointed spaces which sends the vector space V to the block structure space of the projective space of V. We study this functor from the point of view of orthogonal calculus of functors; we show that it is polynomial of degree <= 1 in the sense of orthogonal calculus. This result suggests an attractive description of the block structure space of the infinite dimensional real projective space via the Taylor tower of orthogonal calculus. This space is defined as a colimit of block structure spaces of projective spaces of finite-dimensional real vector spaces and is closely related to some automorphisms spaces of real projective spaces.

Abstract:
We present a classification of fake lens spaces of dimension greater or equal to 5 which have as fundamental group the cyclic group of order N = 2^K, in that we extend the results of Wall and others in the case N=2.

Abstract:
In the first part of the paper we present a classification of fake lens spaces of dimension >= 5 whose fundamental group is the cyclic group of order N >= 2. The classification uses and extends the results of Wall and others in the case N = 2 and N odd and the results of the authors of the present paper in the case N a power of 2. In the second part we study the suspension map between the simple structure sets of lens spaces of different dimensions. As an application we obtain an inductive geometric description of the torsion invariants of fake lens spaces.

Abstract:
For a finite dimensional real vector space V with inner product, let F(V) be the block structure space, in the sense of surgery theory, of the projective space of V. Continuing a program launched in part I, we investigate F as a functor on vector spaces with inner product, relying on functor calculus ideas. It was shown in part I that F agrees with its first Taylor approximation T_1 F (which is a polynomial functor of degree 1) on vector spaces V with dim(V) > 5. To convert this theorem into a functorial homotopy-theoretic description of F(V), one needs to know in addition what T_1 F(V) is when V=0. Here we show that T_1 F(0) is the standard L-theory space associated with the group Z/2, except for a deviation in \pi_0. The main corollary is a functorial two-stage decomposition of F(V) for dim(V) > 5 which has the L-theory of the group Z/2 as one layer, and a form of unreduced homology of RP (V) with coefficients in the L-theory of the trivial group as the other layer. (Except for dimension shifts, these are also the layers in the traditional Sullivan-Wall-Quinn-Ranicki decomposition of F(V). But the dimension shifts are serious and the SWQR decomposition of F(V) is not functorial in V.) Because of the functoriality, our analysis of F(V) remains meaningful and valid when V=R^\infty.

Abstract:
For a closed topological manifold M with dim (M) >= 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure group of M as defined by Ranicki. If dim (M) = 2d-1, M is oriented and M is equipped with a map to the classifying space of a finite group G, then the reduced rho-invariant defines a function, \wrho : S(M) \to \QQ R_{hat G}^{(-1)^d}, to a certain sub-quotient of the complex representation ring of G. We show that the function \wrho is a homomorphism when 2d-1 >= 5. Along the way we give a detailed proof that a geometrically defined map due to Cappell and Weinberger realises the 8-fold Siebenmann periodicity map in topological surgery.

Abstract:
For a space X, we define Frobenius and Verschiebung operations on the nil-terms NA^{fd} (X) in the algebraic K-theory of spaces, in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NA^{fd} (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N_x]-module structure on the homotopy groups of NA^{fd} (X), with N_x the multiplicative monoid. We also we give a calculation of the homotopy groups of the nil-terms NA^{fd} (*) after p-completion for an odd prime p as Z_p[N_x]-modules up to dimension 4p-7. We obtain non-trivial groups only in dimension 2p-2, where it is finitely generated as a Z_p[N_x]-module, and in dimension 2p-1, where it is not finitely generated as a Z_p[N_x]-module.

Abstract:
The total surgery obstruction of a finite n-dimensional Poincare complex X is an element s(X) of a certain abelian group S_n (X) with the property that for n >= 5 we have s(X) = 0 if and only if X is homotopy equivalent to a closed n-dimensional topological manifold. The definitions of S_n (X) and s(X) and the property are due to Ranicki in a combination of results of two books and several papers. In this paper we present these definitions and a detailed proof of the main result so that they are in one place and we also add some of the details not explicitly written down in the original sources.

Abstract:
The automated procedure for the monitoring of the adsorption process in the solute-sorbent-solvent system has been elaborated. It uses commercially available instrument CRYSTAF model 200. The application of CRYSTAF enabled monitoring of adsorption of linear polyethylene with weight average molar masses of 2, 14, and 53 kg/mol from 1,2,4-trichlorobenzene onto zeolite SH-300 at temperature as high as 140°C. It is the authors' understanding that this is the first demonstration of an adsorption isotherms for polyethylene. The measurement with the CRYSTAF instrument reduces manual manipulations with dangerous solvents at high temperature and enables automated long-time monitoring of the concentration of the solute in an adsorption system.

Abstract:
We define debt ratio as the market value of a firm’s debt divided by the market value of the firm. In a perfect market with corporate taxes, given that the cost of debt is increasing and concave up and that the firm rebalances its debt, the cost of equity is an increasing and concave up function of the debt ratio if and only if the third derivative of the cost of debt is non-negative; otherwise, the cost of equity is increasing but its exact shape cannot be ascertained. In all cases, however, the cost of equity must be concave up initially. Also in this world, the weighted average cost of capital of the firm, WACC, is decreasing and concave down. In an imperfect market, the WACC may not have an absolute minimum between zero and 100 percent debt. Even if it does, the minimum may not occur at the debt ratio that maximizes firm value. The “pure-play” method to determine a new project’s discount rate is correct only if the opportunity cost of capital of the comparable firm remains constant with respect to the debt ratio or if the debt ratio of the comparable firm is equal to the target debt ratio of the firm evaluating the project. Strictly speaking, even if the two debt ratios are the same, the opportunity cost of capital of the comparable firm is not necessarily equal to that of the project unless the two costs of capital are identical functions of the debt ratio. Therefore, this method may not be valid.