# Questions tagged [diffeomorphism]

This tag is for questions regarding to "diffeomorphisms", a map between manifolds which is differentiable and has a differentiable inverse.

503 questions
Filter by
Sorted by
Tagged with
1 vote
32 views

### Change of coordinates in a regular surface $S$.

I'm quite confused in the following situation: Suppose that $S \subset \mathbb{R}^3$ is a regular surface. Let $U_1$ and $U_2$ be open sets in $\mathbb{R}^2$, and consider the pair of ...
• 135
37 views

### Why are quasiconformal maps orientation preserving under the analytic definition?

Quasiconformal maps admit a lot of equivalent definitions. One of the geometric definitions states that a homeomorphism $f$ is quasiconformal, iff it preserves orientation and changes the modulie of ...
48 views

### Question about Lemma 19.1 in Munkres' Analysis on Manifolds

In Munkres' Analysis on Manifolds, page 162 Lemma 19.1 Step 2 it states: Third, we check the local finiteness condition. Let $\mathbf{x}$ be a point of $A$. The point $\mathbf{y}=g(\mathbf{x})$ has a ...
• 174
177 views

• 219
36 views

• 2,973
76 views

### A differentiable homeomorphism that isn't a diffeomorphism?

From the book Introduction to Differentiable Topology by TH Brocker and K Janich. 1.7 Definition: A diffeomorphism is an invertible differentiable map Below: A differentiable homeomorphism need not ...
• 1,312
8 views

• 211
72 views

### Extension of Homeomorphism of boundaries

Let $A,B \subset \mathbb{R}^2$ be two open bounded sets with smooth boundary (boundary is a smooth closed curve). Let us assume that we know $$\Phi \colon \partial A \to \partial B$$ is a ...
• 179
16 views

### Locally conjugate diffeomorphisms, but does not take orbits to orbits.

I'm working on the Palis's ''Geometrical Theory of Dynamical Systems''. I have the next problem: Let $X$ and $Y$ be $C^1$ vector fields on $\mathbb{R}^m$. Suppose that $0$ is an attracting hyperbolic ...
1 vote
158 views

### Show that the lens space is a smooth 3-manifold

Suppose we view $S^3\subset C^2$. Then for coprime integers $p,q$ we define the lens space by $M_{p,q}=S^3/\sim$ where $(z_1,z_2)\sim(z_1e^\frac{2\pi i}{p},z_2e^\frac{2\pi iq}{p})$. I want to show ...
• 211