I think there is no conceptual difficulty at here. For his definition of connected sum we have: Two manifolds M 1, M 2 with the same dimension in. Differential Manifolds – 1st Edition – ISBN: , View on ScienceDirect 1st Edition. Write a review. Authors: Antoni Kosinski. differentiable manifolds are smooth and analytic manifolds. For smooth ..  A. A. Kosinski, Differential Manifolds, Academic Press, Inc.
Kosinski Limited preview – Morgan, which discusses the most recent developments in differential topology. Maybe I’m misreading or misunderstanding.
Academic PressDec 3, – Mathematics – pages. In his section on connect sums, Kosinski does differentiao seem to acknowledge that, in the case where the manifolds in question do not admit orientation reversing diffeomorphisms, the topology in fact homotopy type of a connect sum of two smooth manifolds may depend on the particular identification of spheres used to connect the manifolds.
The text is supplemented by numerous interesting historical notes and contains a new appendix, “The Work of Grigory Perelman,” by John W. I think there is no conceptual difficulty at here. My library Help Advanced Book Search.
Sign up using Email and Password. For his definition of connected sum we have: Chapter IX Framed Manifolds. The final chapter introduces the method of surgery and applies it to the classification of smooth structures of spheres. Selected pages Page 3. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and the theory of lie groups.
Post as a guest Name. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individual study.
So if you feel really confused you should consult other sources or even the original paper in some of the topics. The Concept of a Riemann Surface. Contents Chapter I Differentiable Structures. The mistake in the proof seems manfiolds come at the bottom of page 91 when he claims: Presents the study and classification of smooth structures on manifolds It begins with the elements of theory and concludes with an introduction to the method of surgery Chapters contain a detailed presentation of the foundations of differential topology–no knowledge of algebraic topology is required for this self-contained section Chapters begin by explaining the joining of manifolds along submanifolds, and ends with the proof of the h-cobordism theory Chapter 9 presents the Pontriagrin construction, the principle link between differential topology and homotopy theory; The final chapter introduces the method of surgery and applies it to diffferential classification of smooth structures on spheres.