On Thom Spectra, Orientability, and Cobordism (Springer Monographs in Mathematics)

For Many Years, Algebraic Topology Rests On Three Legs: Ordinary Cohomology, K-theory, And Cobordism. This Book Is The First Guide On The Subject Of Cobordism Since R. Stong's Encyclopaedic And Influential Notes Of A Generation Ago. It Concentrates On Thom Spaces (spectra), Orientability Theory And (co)bordism Theory (including (co)bordism With Singularities And, In Particular, Morava K-theories), Framed By (co)homology Theories And Spectra. From The Foreword By Haynes Miller The Author Has Also Performed A Service To The History Of Science In This Book, Giving Detailed Attributions. This Same Care Makes The Book Easy To Use By The Student, For When Proofs Are Not Given, Specific References Are. From The Reviews: … This Is An Important, Formidable Monograph ..... The Readers Interested In Pursuing This Line Of Research Will Find It Enormously Helpful To Have The Results Assembled In One Place With An Unified, Brilliant Exposition. Zentralblatt Math 906.1999 This Book Provides An Excellent And Thorough Treatment Of Various Topics Related To Cobordism. It Should Become An Indispensable Tool For Advanced Graduate Students And Workers In Algebraic Topology. … Mathscinet Mr1627486 Foreword -- Preface -- Introduction -- Chapter I. Notation, Conventions And Other Preliminaries -- Chapter Ii. Spectra And (co)homology Theories -- Chapter Iii. Phantoms -- Chapter Iv. Thom Spectra -- Chapter V. Orientability And Orientations -- Chapter Vi. K And K0-orientability -- Chapter Vii. Complex (co)bordism -- Chapter Viii. (co)bordism With Singularities -- Chapter Ix. Complex (co)bordism With Singularities -- References -- List Of Notations -- Subject Index. Yuli B. Rudyak. Includes Bibliographical References (p. [553]-571) And Index. For many years, algebraic topology rested on three legs: "ordinary" cohomology, K-theory, and cobordism. This book is the first guide in the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions. This same care makes the book easy to use by the student, for when proofs are not given, specific references are. Rudyak’s Groundbreaking Monograph Is The First Guide On The Subject Of Cobordism Since Stong's Influential Notes Of A Generation Ago. It Concentrates On Thom Spaces (spectra), Orientability Theory And (co)bordism Theory (including (co)bordism With Singularities And, In Particular, Morava K-theories). These Are All Framed By (co)homology Theories And Spectra. The Author Has Also Performed A Service To The History Of Science In This Book, Giving Detailed Attributions.