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**14**

votes

**0**answers

337 views

### Do there exist exotic 4-tori?

More precisely: are there known manifolds which are homeomorphic, but not diffeomorphic to the standard 4-torus? Are there any nice invariants distinguishing such manifolds?
Related: if such a ...

**8**

votes

**1**answer

325 views

### Construction of exotic spheres that do not bound parallelizable manifolds

There are at least two ways to construct homotopy spheres that bound parallelizable manifolds, namely Milnor's plumbing construction and Brieskorn's method of singularities, and each of these methods ...

**11**

votes

**1**answer

513 views

### Are there non-compact, non-smoothable manifolds?

There do exist manifolds which do not admit any smooth structure at all. But the only examples I've heard of are all compact.
Are there any non-compact, non-smoothable manifolds?

**4**

votes

**1**answer

184 views

### smooth homotopy on exotic R^4

Take an exotic $\mathbb{R}^4$ i.e. $V = (\mathbb{R}^4,d)$ such that $V$ is not diffeomorphic to $\mathbb{R}^4$ with standard metric.
Is it true (obvious?) that any two smooth maps $f_1, f_2: S^k \to ...

**7**

votes

**5**answers

898 views

### Is there a relation between 4-dimentional general relativity and exotic smooth structures on $\mathbb{R}^4$?

Let's say General Relativity is the study of the Einstein equation on smooth Lorentzian manifolds, i.e. pseudo-Riemanniann manifolds of signature $(n-1,1)$.
I've heard more than once people say that ...