Freeness of equivariant cohomology and mutants of compactified representations

We survey generalisations of the Chang-Skjelbred Lemma for integral coefficients. Moreover, we construct examples of manifolds with actions of tori of rank > 2 whose equivariant cohomology is torsion-free, but not free. This answers a question of Allday's. The "mutants" we construct are obtained from compactified representations and involve Hopf bundles in a crucial way.Comment: 11 pages; more details on the smooth structure of the mutants; other, minor change

Steenrod squares on conjugation spaces

We prove that the coefficients of the so-called conjugation equation for conjugation spaces in the sense of Hausmann-Holm-Puppe are completely determined by Steenrod squares. This generalises a result of V.A. Krasnov for certain complex algebraic varieties. It also leads to a generalisation of a formula given by Borel and Haefliger, thereby largely answering an old question of theirs in the affirmative.Comment: 4 page

Reducing the Excess Burden of Subsidizing the Stork: Joint Taxation, Individual Taxation, and Family Tax Splitting

Analyzing a homogenous household setting with endogenous fertility and endogenous labor supply, we demonstrate that moving from joint taxation to individual taxation and adapting child benefits so as to keep fertility constant entails a Pareto improvement. The change is associated with an increase in labor supply and consumption and a reduction of the marginal income tax, while the child benefit may move in either direction. Similarly, a move from joint taxation to some scheme of family tax splitting increases labor supply and welfare.income taxation, fertility, splitting, labor supply

Pension, Fertility, and Education

A pay-as-you-go pension scheme is associated with positive externalities of having children and providing them with human capital. In a framework with heterogeneity in productivity, and stochastic and endogenous investment in fertility and education, we discuss internalization policies associated with child benefits in the pension formula. The second-best scheme displays both a benefit contingent on the contributions of children and a purely fertility-related component.pay-as-you-go, fertility, human capital, externalities

Operator space structure and amenability for Fig\`a-Talamanca-Herz algebras

Column and row operator spaces - which we denote by COL and ROW, respectively - over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group $G$ and $p,p' \in (1,\infty)$ with $\frac{1}{p} + \frac{1}{p'} = 1$, we use the operator space structure on $CB(COL(L^{p'}(G)))$ to equip the Figa-Talamanca-Herz algebra $A_p(G)$ with an operator space structure, turning it into a quantized Banach algebra. Moreover, we show that, for $p \leq q \leq 2$ or $2 \leq q \leq p$ and amenable $G$, the canonical inclusion $A_q(G) \subset A_p(G)$ is completely bounded (with cb-norm at most $K_G^2$, where $K_G$ is Grothendieck's constant). As an application, we show that $G$ is amenable if and only if $A_p(G)$ is operator amenable for all - and equivalently for one - $p \in (1,\infty)$; this extends a theorem by Z.-J. Ruan.Comment: 25 pages; some minor, hopefully clarifying revision