On K_1 of a Waldhausen category

We give a simple representation of all elements in K_1 of a Waldhausen category and prove relations between these representatives which hold in K_1

Review article on the role of visualisation in mathematics conceptualisation and learning

Visualisation is a natural element at the root of mathematical thought, in the discovery of relations between mathematical objects, and in the transmission and communication of mathematics. This review focuses on the introductory chapter of one of the most famous books on this topic, by a widely published writer on pedagogy of mathematics, discussing at the same time implications for undergraduate teaching in the subject

Unital associahedra

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A-infinity algebras of Fukaya-Oh-Ohta-Ono.Comment: 22 pages, EPS color figure

The Value and Risk of Defined Contribution Pension Schemes: International Evidence

Using data on historical returns on international financial assets, the paper simulates pension fund and pension replacement ratios, building up frequency distributions of these ratios for individuals saving in a defined contribution pension plan in different countries. These frequency distributions illustrate the risk in the pension replacement ratio faced by an individual who saves in a typical defined contribution pension scheme.Risks, Defined contribution pension schemes, pension replacement ratio.

On determinant functors and KK-theory

In this paper we introduce a new approach to determinant functors which allows us to extend Deligne's determinant functors for exact categories to Waldhausen categories, (strongly) triangulated categories, and derivators. We construct universal determinant functors in all cases by original methods which are interesting even for the known cases. Moreover, we show that the target of each universal determinant functor computes the corresponding $K$-theory in dimensions 0 and 1. As applications, we answer open questions by Maltsiniotis and Neeman on the $K$-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional $K$-theory and obtain generators and (some) relations for various $K_{1}$-groups.Comment: 73 pages. We have deeply revised the paper to make it more accessible, it contains now explicit examples and computations. We have removed the part on localization, it was correct but we didn't want to make the paper longer and we thought this part was the less interesting one. Nevertheless it will remain here in the arXiv, in version 1. If you need it in your research, please let us kno

(dme)MCl_3(NNPh_2) (dme= dimethoxyethane; M= Nb, Ta): A Versatile Synthon for [Ta═NNPh_2] Hydrazido(2-) Complexes

Complexes (dme)TaCl_3(NNPh_2) (1) and (dme)NbCl_3(NNPh_2) (2) (dme =1,2-dimethoxyethane) were synthesized from MCl5 and diphenylhydrazine via a Lewis-acid assisted dehydrohalogenation reaction. Monomeric 1 has been characterized by X-ray, IR, UV−vis, ^(1)H NMR, and ^(13)C NMR spectroscopy and contains a κ^(1)-bound hydrazido(2-) moiety. Unlike the corresponding imido derivatives, 1 is dark blue because of an LMCT that has been lowered in energy as a result of an N_(α)−N_(β) antibonding interaction that raises the highest occupied molecular orbital (HOMO). Reaction of 1 with a variety of neutral, mono- and dianionic ligands generates the corresponding ligated complexes retaining the κ^(1)-bound [Ta−NNPh_2] moiety

Annuity Prices, Money's Worth and Replacement Ratios: UK experience 1972 - 2002

In this paper we construct a time series of annuity prices from 1972-2002, and examine whether annuity rates are unfairly priced, and assess the extent to which annuitisation risks are hedged by stock market returns. We find no evidence that the average annuity rate is unfairly low. Depending on the assumptions about future longevity, the present value of an annuity (it's money's worth) is of the order of between 90 per cent and 100 per cent of the purchase price. Compared with the typical costs of buying financial services this figure looks suspiciously good. In addition, we find no reason to suggest that individuals are worse off by annuity rates being low, since this has been off-set by increases in the value of pension funds over the last thirty years. Even apart from the fact that people retiring today expect to live longer, their pension income (compared to their final salary) looks as good as ever.annuities, money's worth, replacement ratios

The Profitability of Block Trades in Auction and Dealer Markets

The paper compares the trading costs for institutional investors who are subject to liquidity shocks, of trading in auction and dealer markets. The batch auction restricts the institutions’ ability to exploit informational advantages because of competition between institutions when they simultaneously submit their orders. This competition lowers aggregate trading costs. In the dealership market, competition between traders is absent but trades occur in sequence so that private information is revealed by observing the flow of successive orders. This information revelation reduces trading costs in aggregate. We analyse the relative effects on profits of competition in one system and information revelation in the other and identify the circumstances under which dealership markets have lower trading costs than auction markets and vice versa.Market microstructure, Auction market, Dealer markets.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.Comment: Last version before publication. To appear in Journal of Noncommutative Geometry. 57 page