2,075 research outputs found

    Quasisymmetric functions from a topological point of view

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    It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions, Symm. We offer the cohomology of the loop space of the suspension of the infinite complex projective space as a topological model for the ring of quasisymmetric functions, QSymm. We exploit standard results from topology to shed light on some of the algebraic properties of QSymm. In particular, we reprove the Ditters conjecture. We investigate a product on the loop space that gives rise to an algebraic structure which generalizes the Witt vector structure in the cohomology of BU. The canonical Thom spectrum over the loops on the suspension of BU(1) is highly non-commutative and we study some of its features, including the homology of its topological Hochschild homology spectrum.Comment: Slightly revised version; to appear in Mathematica Scandinavic

    Invertible modules for commutative S\mathbb{S}-algebras with residue fields

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    The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules over the coefficient ring by taking homotopy groups. If a connective commutative S-algebra R has coherent localizations (R_*)_m for every maximal ideal m in R_*, then for every invertible R-module U, U_* is an invertible graded R_*-module. In some non-connective cases we can carry the result over under the additional assumption that the commutative S-algebra has `residue fields' for all maximal ideals m in R_* if the global dimension of R_* is small or if R is 2-periodic with underlying Noetherian complete local regular ring R_0.Comment: Revised version. One serious flaw correcte

    A Time-Frequency Analysis of the Coherences of the US Business

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    The dating of a possible European business cycle has been inconclusive. At this stage, there is no consensus on the existence of such a cycle, or of its periodicity and amplitude, or of the relationship of individual member countries to that cycle. Yet cyclical convergence is the key consideration for countries that wish to be members of the currency union. The confusion over whether and to what degree the UK is converging on the cycles of her European partners, or whether her cycle is more in line with the US, is an example of this lack of consensus. We show that countries will vary in the components and characteristics that make up their output cycles, as well as in the state of their cycle at any point of time. Next, we show how to decompose a business cycle in a time-frequency framework. This allows us to decompose movements in output, both at the European level and in member countries, into their component cycles and allows those component cycles to vary in importance and cyclical characteristics over time. It also allows us to determine if the inconclusive convergence results so far have appeared because member countries have some cycles in common, but diverge at other frequenciesTime-Frequency Analysis, Coherence, Growth Rates, Business Cycle

    Trans-Pacific Economic Relations and US-China Business Cycles: Convergence within Asia versus US Economic Leadership

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    This paper tests the hypothesis that the links and leadership/dependency relationships between the People’s Republic of China (PRC), the United States (US), and the other large Asian economies have changed over the past 20 years with the industrialization of the PRC economy. We use time-varying spectral methods to decompose the links between seven advanced Asian economies and the US. We find: (a) the links with the US have been weakening, while those within a bloc based on the PRC have strengthened; (b) that this is not new—it has been happening since the 1980s, but has been partly reversed by the recent surge in trade; (c) that there are two blocs within the Asian economic area: one based on Japan and the Republic of Korea and the other on the PRC and her satellites; (d) that product composition is responsible for this division (and for some movement between the blocs); and (e) that the links between the PRC and the US are rather complex, with the US able to shape the cycles elsewhere through her control of monetary conditions, but the PRC able to control the size of the cycles at home and (to some extent) abroad.trans-pacific economic relations; us-china trade; us economic leadership; industrialization prc economy; advanced asian economies

    Time Varying Cyclical Analysis for Economies in Transition

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    The identification of a possible European business cycle has been inconclusive and is complicated by the enlargement to the new member states and their transition to market economies. This paper shows how to decompose a business cycle into a time-frequency framework in a way that allows us to accommodate structural breaks and nonstationary variables. To illustrate, calculations of the growth rate spectrum and coherences for the Hungarian, Polish, German and French economies show the instability of the transition period. However, since then there has been convergence on the Eurozone economy at short cycle lengths, but little convergence in long cycles. We argue that this shows evidence of nominal convergence, but little real convergence. The Maastricht criteria for membership of the Euro therefore need to be adapted to test for real convergence.Time-Frequency Analysis, Coherence, Growth Rates, Business Cycle
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