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PREFACE One of the principal aims of this study is to understand spaces which carry metrics of positive scalar curvature. In recent years this subject has been the focus of lively research, and we would like to begin with a brief discussion of the developments (1). Certainly, one of the simplest invariants of a riemannian manifold is its scalar curvature(More)
Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that(More)
This is the second of two papers concerned with the situation in which the injectivity radius at certain points of a riemannian manifold is "small" compared to the curvature. In Part I [3], we introduced the concept of an F-structure of positive rank. This generalizes the notion of a torus action, for which all orbits have positive dimension. We showed that(More)
Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that(More)
Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that(More)
We give a mechanical recipe for creating simple face-pairing descriptions of closed 3-manifolds. We call the technique twisted face-pairing. Among the simpler twisted face-pairings we have studied, we have discovered manifolds (usually infinite classes of man-ifolds) which admit geometries based on S 3 , H 3 , Solv, Nil, and the universal cover of P SL(2,(More)
We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i)(More)
This a brief introduction to the formal genetics centered around two mathematical ideas going back to Gregor Mendel and Alfred Sturtevant. Preambule. The road from biology (or from any branch of science on the fundamental level) to mathematics goes in several (often Brownian rather than straight) paths in parallel. • Identifying a class of phenomena– "(More)
We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i)(More)