Typological parameters of genericity

Different languages employ different morphosyntactic devices for expressing genericity. And, of course, they also make use of different morphosyntactic and semantic or pragmatic cues which may contribute to the interpretation of a sentence as generic rather than episodic. [...] We will advance the strong hypo thesis that it is a fundamental property of lexical elements in natural language that they are neutral with respect to different modes of reference or non-reference. That is, we reject the idea that a certain use of a lexical element, e.g. a use which allows reference to particular spatio-temporally bounded objects in the world, should be linguistically prior to all other possible uses, e.g. to generic and non-specific uses. From this it follows that we do not consider generic uses as derived from non-generic uses as it is occasionally assumed in the literature. Rather, we regard these two possibilities of use as equivalent alternative uses of lexical elements. The typological differences to be noted therefore concern the formal and semantic relationship of generic and non-generic uses to each other; they do not pertain to the question of whether lexical elements are predetermined for one of these two uses. Even supposing we found a language where generic uses are always zero-marked and identical to lexical sterns, we would still not assume that lexical elements in this language primarily have a generic use from which the non-generic uses are derived. (Incidentally, none of the languages examined, not even Vietnamese, meets this criterion.

On 4-Manifolds, Folds and Cusps

We study simple wrinkled fibrations, a variation of the simplified purely wrinkled fibrations introduced by Williams, and their combinatorial description in terms of surface diagrams. We show that simple wrinkled fibrations induce handle decompositions on their total spaces which are very similar to those obtained from Lefschetz fibrations. The handle decompositions turn out to be closely related to surface diagrams and we use this relationship to interpret some cut-and-paste operations on 4-manifolds in terms of surface diagrams. This, in turn, allows us classify all closed 4-manifolds which admit simple wrinkled fibrations of genus one, the lowest possible fiber genus.Comment: 38 pages, 17 Figure

The Goodwillie tower for S^1 and Kuhn's theorem

We analyze the homological behavior of the attaching maps in the 2-local Goodwillie tower of the identity evaluated at S^1. We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S^1 at the prime 2.Comment: v2: 23 pages, clarified exposition in many parts, to appear in AG

Some root invariants at the prime 2

The first part of this paper consists of lecture notes which summarize the machinery of filtered root invariants. A conceptual notion of "homotopy Greek letter element" is also introduced, and evidence is presented that it may be related to the root invariant. In the second part we compute some low dimensional root invariants of v_1-periodic elements at the prime 2.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200