Involutions on Four-manifolds [microform]
Author | : Jastrzebowski, Wojciech Z |
Publisher | : Ann Arbor, Mich. : University Microfilms International |
Total Pages | : 88 |
Release | : 1993 |
Genre | : Four-manifolds (Topology) |
ISBN | : |
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Author | : Jastrzebowski, Wojciech Z |
Publisher | : Ann Arbor, Mich. : University Microfilms International |
Total Pages | : 88 |
Release | : 1993 |
Genre | : Four-manifolds (Topology) |
ISBN | : |
Author | : Wojciech Z. Jastrzebowski |
Publisher | : |
Total Pages | : 88 |
Release | : 1993 |
Genre | : Four-manifolds (Topology) |
ISBN | : |
Author | : Santiago Lopez de Medrano |
Publisher | : Springer Science & Business Media |
Total Pages | : 114 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642650120 |
This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.
Author | : D. S. Freed |
Publisher | : Springer Science & Business Media |
Total Pages | : 242 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468402587 |
This book is the outcome of a seminar organized by Michael Freedman and Karen Uhlenbeck (the senior author) at the Mathematical Sciences Research Institute in Berkeley during its first few months of existence. Dan Freed (the junior author) was originally appointed as notetaker. The express purpose of the seminar was to go through a proof of Simon Donaldson's Theorem, which had been announced the previous spring. Donaldson proved the nonsmoothability of certain topological four-manifolds; a year earlier Freedman had constructed these manifolds as part of his solution to the four dimensional ; Poincare conjecture. The spectacular application of Donaldson's and Freedman's theorems to the existence of fake 1R4,s made headlines (insofar as mathematics ever makes headlines). Moreover, Donaldson proved his theorem in topology by studying the solution space of equations the Yang-Mills equations which come from ultra-modern physics. The philosophical implications are unavoidable: we mathematicians need physics! The seminar was initially very well attended. Unfortunately, we found after three months that we had covered most of the published material, but had made little real progress towards giving a complete, detailed proof. Mter joint work extending over three cities and 3000 miles, this book now provides such a proof. The seminar bogged down in the hard analysis (56 59), which also takes up most of Donaldson's paper (in less detail). As we proceeded it became clear to us that the techniques in partial differential equations used in the proof differ strikingly from the geometric and topological material.
Author | : Iain Roderick Aitchison |
Publisher | : |
Total Pages | : 224 |
Release | : 1979 |
Genre | : Manifolds (Mathematics) |
ISBN | : |
Author | : Ellen Rose Stone |
Publisher | : |
Total Pages | : 86 |
Release | : 1972 |
Genre | : Involutes (Mathematics) |
ISBN | : |
Author | : Santiago López de Medrano |
Publisher | : |
Total Pages | : 102 |
Release | : 195? |
Genre | : Manifolds (Mathematics) |
ISBN | : 9780387050928 |
Author | : |
Publisher | : Academic Press |
Total Pages | : 477 |
Release | : 1972-09-29 |
Genre | : Mathematics |
ISBN | : 0080873596 |
Introduction to Compact Transformation Groups
Author | : Leonor Godinho |
Publisher | : Springer |
Total Pages | : 476 |
Release | : 2014-07-26 |
Genre | : Mathematics |
ISBN | : 3319086669 |
Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.