Surgery Theory: Foundations
This is a webpage for our book project on surgery theory. The book is under construction. At the moment the material is to be used at own risk.
For technical reasons the new versions starting November 2020 will be posted at the webpage
The older versions are kept online here as well for the record and comparison.
Version 09-2020 is from September 3rd, 2020. The chapters 1-11 and 13-14 are already in a reasonable shape. The remaining chapters are preliminary. It is a medium size update of the previous version from 2019. There is a new Chapter 13 about Chain complexes that was created by separating the Appendix from the previous Chapter 13 which is now Chapter 14 and adding a more detailed account of homotopy theory for chain complexes. Also the numbering of all subsequent chapters was increased by 1. In the current Chapter 14 about Algebraic surgery changes were made to make the notation throughout the book more compatible and some material about applications was added. In Chapter 3 some material about Modified surgery (alias Kreck surgery) was added and Chapter 11 was brought up-to-date by including the results made after the year 2000. Hence Chapters 1-11 and 13-14 are close to a final version. The material in Chapters 12 and 15-18 will be gradually polished.
Previous version is from December 19th, 2019. It is a major update from the previous version from 2018. Chapters 9-11 and 13 have been improved and polished and are close to a final version. Chapters 15 and 16 are new. The material in Chapters 12 and 14-17 will be gradually polished.
Version from November 7th, 2018 was a major update from the previous version from 2015. The chapters have been reorganised and renumbered and a substantial amount of material has been added. It includes a new treatment of Poincare duality, of the Spivak normal fibration, of what we call intrinsic surgery obstructions which are related to Poincare duality with local coefficient systems and a revision of both chapters about surgery obstructions (even and odd case).
The older versions are kept online for comparison.
Comments are welcome per email to any of us!