11,296 research outputs found
Branched Coverings, Triangulations, and 3-Manifolds
A canonical branched covering over each sufficiently good simplicial complex
is constructed. Its structure depends on the combinatorial type of the complex.
In this way, each closed orientable 3-manifold arises as a branched covering
over the 3-sphere from some triangulation of S^3. This result is related to a
theorem of Hilden and Montesinos. The branched coverings introduced admit a
rich theory in which the group of projectivities plays a central role.Comment: v2: several changes to the text body; minor correction
The Role of Ontogeny in the Evolution of Human Cooperation
To explain the evolutionary emergence of uniquely human skills and motivations for cooperation, Tomasello et al. (2012, in Current Anthropology 53(6):673â92) proposed the interdependence hypothesis. The key adaptive context in this account was the obligate collaborative foraging of early human adults. Hawkes (2014, in Human Nature 25(1):28â48), following Hrdy (Mothers and Others, Harvard University Press, 2009), provided an alternative account for the emergence of uniquely human cooperative skills in which the key was early human infantsâ attempts to solicit care and attention from adults in a cooperative breeding context. Here we attempt to reconcile these two accounts. Our composite account accepts Hrdyâs and Hawkesâs contention that the extremely early emergence of human infantsâ cooperative skills suggests an important role for cooperative breeding as adaptive context, perhaps in early Homo. But our account also insists that human cooperation goes well beyond these nascent skills to include such things as the communicative and cultural conventions, norms, and institutions created by later Homo and early modern humans to deal with adult problems of social coordination. As part of this account we hypothesize how each of the main stages of human ontogeny (infancy, childhood, adolescence) was transformed during evolution both by infantsâ cooperative skills âmigrating upâ in age and by adultsâ cooperative skills âmigrating downâ in age
The Singular Supports of IC sheaves on Quasimaps' Spaces are Irreducible
Let be a smooth projective curve of genus 0. Let be the variety of
complete flags in an -dimensional vector space . Given an -tuple
of positive integers one can consider the space of
algebraic maps of degree from to . This space admits some
remarkable compactifications (Quasimaps),
(Quasiflags) constructed by Drinfeld and Laumon respectively. In [Kuznetsov] it
was proved that the natural map is a small
resolution of singularities. The aim of the present note is to study the
singular support of the Goresky-MacPherson sheaf on the Quasimaps'
space . Namely, we prove that this singular support
is irreducible. The proof is based on the factorization property of Quasimaps'
space and on the detailed analysis of Laumon's resolution .Comment: 8 pages, AmsLatex 1.
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