Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds

We show that there exists a metric with positive scalar curvature on S2xS1 and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborhood of a strictly stable 2-sphere, is smooth except at two helicoid-like singularities on the 2-sphere. The construction is inspired by a recent example by D. Hoffman and B. White.Comment: 12 pages, 3 figures, replaced because of corrupted fil

On an extension of the notion of Reedy category

We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occuring in topology such as Segal's category Gamma, or the total category of a crossed simplicial group such as Connes' cyclic category Lambda. For any generalized Reedy category R and any cofibrantly generated model category E, the functor category E^R is shown to carry a canonical model structure of Reedy type

A thought model for the fracture of brittle solids

Translation of Ein Gedankenmodell für den Zerreißvorgang spröder Körper, published in Zeitschrift für angewandte Mathematik und Mechanik, 13:2, (1933), pp.129-133

On topics today

This article surveys the state of so-called topic theory today. It charts its development through two generations of topic theorists. The first is constructed around three influential texts: Leonard Ratners seminal book that established the discipline in its own right, Classic music: expression, form and style (1980); Wye Allanbrooks. Rhythmic gesture in Mozart: Le nozze di Figaro and Don Giovanni (1983); and Kofi Agawus. Playing with signs: a semiotic interpretation of classical music (1991). The second comprises significant advances in topic theory essayed through two further pairs of texts: Robert Hattens Musical meaning in Beethoven: markedness, correlation, and interpretation (1994) and Interpreting musical gestures, topics, and tropes: Mozart, Beethoven, Schubert (2004); and Raymond Monelles Linguistics and semiotics in music (1992) and The sense of music: semiotic essays (2000). Topic Theory's role as the soft hermeneutic sub-field of music semiotics (relative to the harder, formalist practices of Nattiezs neutral level analysis) is portrayed here as navigating a number of treacherous polemical paths. These wend their way between referential style (expression) and structural syntax (form); historical reconstruction and hermeneutic construction; and heightened sensitivity to social meanings and imposed acts of creative interpretation. This existence of topic theory in a continuous dialogue between structural formalism and the semantics of expressive discourse is held responsible for its marginal position both to the dominant strains of contemporary postmodern musicology and to the dying embers of formalist analysis. The failure of topic theory to strike a fashionable text-context balance thus highlights why musicology continues to view semiotics with scepticism. Ratner presents his thesaurus of style labelssomewhat dubiouslyas the historically authentic ready-to-hand materials (types and styles) of eighteenth-century expressive musical rhetoric. But it is Agawus combination of this universe of topics with a Schenker-influenced beginning-middle-end paradigm that establishes the hallmark of first generation topic theory on which the first half of this paper focuses. Agawus delicate equation between extroversive and introversive semiosis is essayed as a pivotal turning point in topic theorys ability to transcend the mere passive ascription of rhetorical labels. Out of this equation, expressive meanings can ariseas much from the non-congruence, as the congruence, of signs and structure. Hatten's critique of Agawu for neglecting the full interpretative consequences of his signifieds is the springboard for his more hermeneutically replete brand of topic theory and the emergence of the second generation topic theorists. Hattens use of troping (a kind of musical metaphor), is one of many interpretative tools that are responsible for broadening the arena of topic theorysome of his others being: expressive genres, emergent meanings and markedness theory. These are deployed across a variety of musical parameters as Hattens attention increasingly turns to the prototypicality of topics in their euphoric and dysphoric states. Hattens interpretative work is shown to transcend historical reconstruction to comprise creative interpretation built on a much broader definition of expressive gestures, of which topics are only a constituent part. The article concludes with Monelles expos of the dubious historical underpinnings of Ratners topic theory foundations. This does not render this vibrant branch of semiotics redundant but, on the contrary, charts its future direction as one calling out for far deeper historical investigation and cultural criticism. Monelles enlightening forays into the more replete expressive meanings of such topics as the horse and pianto make this point abundantly clear. The future of topics today, if not musicology in general, is one of cultural criticism

Asymptotic flexibility of globally hyperbolic manifolds

In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.Comment: 2 pages, submitted to 'Mathematische Zeitschrift

The mean king's problem: Spin 1

We show how one can ascertain the values of four mutually complementary observables of a spin-1 degree of freedom.Comment: to appear in Zeitschrift fur Naturforschung,3 page

The Lefschetz-Lunts formula for deformation quantization modules

We adapt to the case of deformation quantization modules a formula of V. Lunts who calculates the trace of a kernel acting on Hochschild homology.Comment: 19 pages; Mathematische Zeitschrift 201

On degenerations of plane Cremona transformations

This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.Comment: 21 pages, corrected typos and Proposition 3.21, Mathematische Zeitschrift, published online on 2015/9/2

Reconstructions of a Republic. The political culture of ancient Rome and the research of the last decade.

Review of (K. J.) Hölkeskamp Rekonstruktionen einer Republik. Die politische Kultur des antiken Rom und die Forschung der letzten Jahrzehnte (Historische Zeitschrift Beiheft 38). Pp. 146. Munich: R. Oldenbourg Verlag, 2004. ISBN: 3-486-64439-4