Differentiable Periodic Maps
Author | : Pierre E. Conner |
Publisher | : Springer Science & Business Media |
Total Pages | : 155 |
Release | : 2013-12-14 |
ISBN-13 | : 9783662416334 |
ISBN-10 | : 3662416336 |
Rating | : 4/5 (36 Downloads) |
Download or read book Differentiable Periodic Maps written by Pierre E. Conner and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research tract contains an exposition of our research on bordism and differentiable periodic maps done in the period 1960-62. The research grew out of the conviction, not ours alone, that the subject of transformation groups is in need of a large infusion of the modern methods of algebraic topology. This conviction we owe at least in part to Armand Borel; in particular Borel has maintained the desirability of methods in transformation groups that use differentiability in a key fashion [9, Introduction], and that is what we try to supply here. We do not try to relate our work to Smith theory, the homological study of periodic maps due to such a large extent to P. A. Smith; for a modern development of that subject which expands it greatly see the Borel Seminar notes [9]. It appears to us that our work is independent of Smith theory, but in part inspired by it. We owe a particular debt to G. D. Mostow, who pointed out to us some time ago that it followed from Smith theory that an involution on a compact manifold, or a map of prime period [italic lowercase]p on a compact orientable manifold, could not have precisely one fixed point. It was this fact that led us to believe it worthwhile to apply cobordism to periodic maps.