On Thom Spectra, Orientability, and Cobordism

ISBN-13: 9783642082832 / Angielski / Miękka / 2010 / 590 str.

Yu B. Rudyak

Opis

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

Recenzje

From the reviews of the first printing:

"... This is an important, formidable monograph in the area of algebraic and geometric topology. 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."

C.Costinescu, Zentralblatt Math 906.1999

"This book provides an excellent and thorough treatment of various topics related to cobordosm. It should become an indispensable tool for advanced graduate students and workers in algebraic topology. ..."

D.M.Davis, MathSciNet MR1627486 (99f:550001)

".... The book is indispensable for research workers in algebraic topology. The presentation of the material is very nice and thorough, and this makes the book convenient for students with preliminary knowledge of algebraic topology. ..."

EMS - European Mathematical Society Newsletter December 1999

 

Spis treści

Notation, Conventions and Other Preliminaries.- Spectra and (Co)homology Theories.- Phantoms.- Thom Spectra.- Orientability and Orientations.- K- and KO-Orientability.- Complex (Co)bordism.- (Co)bordism with Singularities.- Complex (Co)bordism with Singularities.