## 543 Citations

### Generation of Source Terms in General Relativity by differential structures

- Mathematics
- 1997

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

- Mathematics
- 2021

. 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

- Mathematics
- 2018

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

- Mathematics
- 2016

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

- Mathematics
- 2016

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

- MathematicsEnsaios Matemáticos
- 2016

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

- Mathematics
- 2015

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

- Mathematics
- 2015

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

- Mathematics
- 2015

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…

## References

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### Quelques propriétés globales des variétés différentiables

- Mathematics
- 1954

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

### Topology of Fibre Bundles

- Mathematics
- 1951

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