Algebraic topology - Errata by Allen Hatcher

By Allen Hatcher

Show description

Read or Download Algebraic topology - Errata PDF

Similar topology books

Selectors

Although the quest for solid selectors dates again to the early 20th century, selectors play an more and more very important function in present study. This publication is the 1st to gather the scattered literature right into a coherent and chic presentation of what's identified and confirmed approximately selectors--and what is still came upon.

From Topology to Computation: Proceedings of the Smalefest

A rare mathematical convention was once held 5-9 August 1990 on the collage of California at Berkeley: From Topology to Computation: solidarity and variety within the Mathematical Sciences a world study convention in Honor of Stephen Smale's sixtieth Birthday the themes of the convention have been a few of the fields within which Smale has labored: • Differential Topology • Mathematical Economics • Dynamical structures • concept of Computation • Nonlinear useful research • actual and organic functions This publication includes the complaints of that convention.

Applications of Contact Geometry and Topology in Physics

Even if touch geometry and topology is in short mentioned in V I Arnol'd's e-book "Mathematical equipment of Classical Mechanics "(Springer-Verlag, 1989, 2d edition), it nonetheless continues to be a site of analysis in natural arithmetic, e. g. see the new monograph by means of H Geiges "An advent to touch Topology" (Cambridge U Press, 2008).

Why Prove it Again?: Alternative Proofs in Mathematical Practice

This monograph considers numerous recognized mathematical theorems and asks the query, “Why end up it back? ” whereas interpreting substitute proofs. It explores different rationales mathematicians can have for pursuing and providing new proofs of formerly verified effects, in addition to how they pass judgement on even if proofs of a given outcome are assorted.

Additional info for Algebraic topology - Errata

Sample text

5, the conclusion follows. 3. This follows by a similar argument. The hypothesis on the manifold guarantees that every map into a sphere of the same dimension is null-homotopic. § 4. Which homotopy spheres bound parallelizable manifolds? Define a subgroup bPn+1 ⊂ Θn as follows. A homotopy n-sphere M represents an element of bPn+1 if and only if M is a boundary of a parallelizable manifold. We will see that this condition depends only on the August 26, 2009 16:21 18 9in x 6in b789-ch02 M. Kervaire and J.

8. M. Kervaire. Relative characteristic classes, Amer. J. Math. 79 (1957), 517–558. 9. M. Kervaire. An interpretation of G. Whitehead’s generalization of the Hopf invariant, Ann. Math. 69 (1959), 345–364. 10. M. Kervaire. A note on obstructions and characteristic classes, Amer. J. Math. 81 (1959), 773–784. 11. M. Kervaire. Some non-stable homotopy groups of Lie groups, Illinois J. Math. 4 (1960), 161–169. 12. M. Kervaire. A manifold which does not admit any differentiate structure, Comment. Math.

Thus j(α) can be chosen so that −l < l − lj(α) ≤ l. This choice of j(α) will guarantee an improvement except in the special case where l happens to be divisible by l. Our progress so far can be summarized as follows. 3. Let M be a framed (k − 1)-connected manifold of dimension 2k + 1 with odd k, k > 1, such that Hk M is finite. Let χ(ϕ, F ) be a framed modification of M which replaces the element λ ∈ Hk M of order l > 1 by an element λ ∈ Hk M of order ±l . If l ≡ 0 mod l, then it is possible to choose (α) ∈ πk (SOk+1 ) so that the modification χ(ϕ) can still be framed, and so that the group Hk Mα is definitely smaller than Hk M .

Download PDF sample

Rated 4.80 of 5 – based on 23 votes