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Euclidean Models of Projective Spaces

Euclidean Models of Projective Spaces I. M. JAMES In this article I have tried to describe, fairly briefly, what is known about the minimum dimension of euclidean space in which projective spaces, of various dimensions, can be (i) embedded, (ii) immersed. The bibliography, which I hope is tolerably complete, gives an idea of the amount of interest there has been in problems of this kind over the past 30 years or so. For reasons of space it is impossible to give a step-by-step account of the progress of the subject. Instead I have attempted, in the first half of this article, to put down a few words about each of the lines of approach which it seems essential to mention, and in the second half to summarize the present position, so far as specific results are concerned. References to the literature are given to assist the reader in search of further details, and do not necessarily include everything on a particular subject. I am most grateful to Professor S. Gitler, Professor K. Y. Lam, Dr. E. Rees and Dr. B. F . Steer for having read this article at the preprint stage; their comments have led to a number of improvements. The table at http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Euclidean Models of Projective Spaces

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/3.3.257
Publisher site
See Article on Publisher Site

Abstract

I. M. JAMES In this article I have tried to describe, fairly briefly, what is known about the minimum dimension of euclidean space in which projective spaces, of various dimensions, can be (i) embedded, (ii) immersed. The bibliography, which I hope is tolerably complete, gives an idea of the amount of interest there has been in problems of this kind over the past 30 years or so. For reasons of space it is impossible to give a step-by-step account of the progress of the subject. Instead I have attempted, in the first half of this article, to put down a few words about each of the lines of approach which it seems essential to mention, and in the second half to summarize the present position, so far as specific results are concerned. References to the literature are given to assist the reader in search of further details, and do not necessarily include everything on a particular subject. I am most grateful to Professor S. Gitler, Professor K. Y. Lam, Dr. E. Rees and Dr. B. F . Steer for having read this article at the preprint stage; their comments have led to a number of improvements. The table at

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Nov 1, 1971

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