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. “How useful it is,” noted the Bulletin of the American Mathematical Society, “to have a single, short, well-written book on differential topology.” This accessible.
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This seems like such an egregious error in such an otherwise solid book that I felt I should ask if anyone has noticed to be sure I’m not misunderstanding something basic. In his section on connect sums, Kosinski does not 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.
His definition of connect sum is as follows. The mistake in the proof seems to come at the bottom of page 91 when he claims: Later on page 95 he claims in Theorem 2. An orientation reversing differeomorphism of the real line which we use to induce an orientation reversing differeomorphism of the Euclidean space minus a point. I disagree that Kosinski’s book is solid though. So if you feel really confused you should consult other sources or even the original paper in some of the topics.
Conceptual error in Kosinski’s “Differential Manifolds”? – Mathematics Stack Exchange
Home Questions Tags Users Unanswered. As the textbook says on the bottom of pg 91 at least in my editionthe existence of your g comes from Theorem 3.
This has nothing to do with orientations. Yes but as I read theorem 3. Maybe I’m misreading or misunderstanding.
I think there is no conceptual difficulty at here. For his definition of connected sum we have: Bombyx mori 13k 6 28 Do you maybe have an erratum of the book?
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