On Manifolds Homeomorphic to the 7-Sphere

  title={On Manifolds Homeomorphic to the 7-Sphere},
  author={John W. Milnor},
  journal={Annals of Mathematics},
  • J. Milnor
  • Published 1 September 1956
  • Mathematics
  • Annals of Mathematics

A classification of $S^3$-bundles over $S^4$

Generation of Source Terms in General Relativity by differential structures

In this paper the relation between the choice of a differential structure and a smooth connection in the tangential bundle is discussed. In the case of four dimensions we obtain a correction of the

The symmetric Kazdan-Warner problem and applications

. After R. Schoen completed the solution of the Yamabe problem, compact manifolds could be allocated in three classes depending on whether they admit a metric with positive, non-negative or only

Disconnecting the moduli space of G_2-metrics via U(4)-coboundary defects

We exhibit examples of closed Riemannian 7-manifolds with holonomy G_2 such that the underlying manifolds are diffeomorphic but whose associated G_2-structures are not homotopic. This is achieved by

On the uniqueness of the smooth structure of the 61-sphere

We prove that the 61-sphere has a unique smooth structure. Following results of Moise [35], Kervaire-Milnor [25], Browder [10] and Hill-Hopkins-Ravenel [19], we show that the only odd dimensional

The triviality of the 61-stem in the stable homotopy groups of spheres

We prove that the 2-primary $\pi_{61}$ is zero. As a consequence, the Kervaire invariant element $\theta_5$ is contained in the strictly defined 4-fold Toda bracket $\langle 2, \theta_4, \theta_4,

Signatures in algebra, topology and dynamics

We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an

Orientation Reversing Gauge Transformations

I investigate whether or not a vector bundle admits an orientation reversing gauge transformation (aka. bundle automorphism). I introduce principal bundles and an equivariant formulation to aid the

Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic

Inertia groups of high dimensional complex projective spaces

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in



Quelques propriétés globales des variétés différentiables

Le présent article donne la démonstration des résultats que j'ai annoncés dans quatre Notes aux Comptes-Rendus [28]1). Il est divisé en quatre chapitres. Le premier chapitre élabore une technique

Relations between the numbers of critical points of a real function of n independent variables

  • Trans. Amer. Math. Soc.,
  • 1925

The Topology of Fibre Bundles. (PMS-14)

Topology of Fibre Bundles

Fibre bundles, an integral part of differential geometry, are also important to physics. This text, a succint introduction to fibre bundles, includes such topics as differentiable manifolds and

Ueber die quaternionalen projektiven Rdume, S.-Ber

  • math. naturw. KI. Bayer. Akad. Wiss. Mifnchen
  • 1953

Sur les classes caracteristiques des structures fibrees spheriques

  • Sur les classes caracteristiques des structures fibrees spheriques
  • 1952