## Simple-connectivity of the Browder-Novikov theorem |

### From inside the book

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... (i.e. tt T(f) > H T(f) is surjective for + dim f) . toting one of our combinatorial

manifolds by M, we prove that SM, the suspension is a spherical top homology

class, so that the

hypothesis.

... (i.e. tt T(f) > H T(f) is surjective for + dim f) . toting one of our combinatorial

manifolds by M, we prove that SM, the suspension is a spherical top homology

class, so that the

**trivial**real line bundle over M ss the Browder-Novikovhypothesis.

Page

... T(f) has a spherical top homology class (i.e. tt T(f) > H T(f) is surjective for q =

2n+l + dim f) . Denoting one of our combinatorial manifolds by M, we prove that

SM, the suspension of M, has a spherical top homology class, so that the

real ...

... T(f) has a spherical top homology class (i.e. tt T(f) > H T(f) is surjective for q =

2n+l + dim f) . Denoting one of our combinatorial manifolds by M, we prove that

SM, the suspension of M, has a spherical top homology class, so that the

**trivial**real ...

Page 4

Now, since HT1 = Z, there Is a map M > S whose composition with the inclusion S

> M Is homotopic to the identity S > S . Taking the suspension of these 2 maps we

see that S is a retract of M . It follows that the attaching map f is

Now, since HT1 = Z, there Is a map M > S whose composition with the inclusion S

> M Is homotopic to the identity S > S . Taking the suspension of these 2 maps we

see that S is a retract of M . It follows that the attaching map f is

**trivial**, and thus ...### What people are saying - Write a review

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### Common terms and phrases

2n+2 SM 2n+l a e H abelian argument assume boundary Browder Browder-Novikov c2 c2n+l calculate cell closed differential manifold combinatorial equivalence combinatorial manifold complex construct copies curve D2n x Sl denote diffeomorphic differentiable imbedding differential structure divisible by t-l element elementary ideal Essential f(S2n_l fact finite follows fundamental given hence homotopy type identified identity imbed imbedded sphere inclusion induced infinite integer intersection coefficient intersection number intersection point inverse image isomorphic knot Lemma on normal M2n+l modification module normal bundle normal field normal vector field Novikov obtained obvious permutation Poincare duality pole presentation for H proof proved pushed relation matrix rely represented Robertello's S2n+l shows similar simply-connected Smale theory space spherical top homology surjective suspension symmetric tangent bundle theorem top homology class transversally trivial tubular usual values Y,bY Z[J]-module