# Tagged Questions

**11**

votes

**3**answers

602 views

### Is the class of n-dimensional manifolds essentially small?

Question: Consider the proper class of all $n$-dimensional smooth manifolds. If we take the equivalence classes where two manifolds are identified if there exists a diffeomorphism between them, is ...

**8**

votes

**3**answers

342 views

### Configuration spaces of the torus

I would like a reference that calculates the rational homology of the unordered configuration spaces of the torus.

**10**

votes

**1**answer

445 views

### Strong Whitney embedding theorem for non-compact manifolds

$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact manifolds.
The strong ...

**8**

votes

**1**answer

355 views

### Waldhausen $K$-theory for $G$-spaces

I would guess that the following is true, and that somebody has worked it out, but I don't recall ever seeing it. Can anyone point me to any literature on it?
Let $G$ be a finite group. We know that ...

**4**

votes

**1**answer

354 views

### complex manifold with corner

I was reading Dominic Joycee article on Manifold with corner. He talk about manifold with corner modeled over $[0,\infty)^k\times \mathbb R^{n-k}$ for some $k\leq n$. From here i moved to Melrose ...

**5**

votes

**1**answer

754 views

### Classification of smooth atlases

Let $\mathcal{A}$ be a smooth maximal atlas on a manifold $M$. Let $f:M\to M$ be a smooth invertible function, whose inverse is not smooth (for example $f:\mathbb R\to \mathbb R$, $f(x)=x^3$). Then ...

**4**

votes

**2**answers

1k views

### On the smooth structure of the spaces of $k$-jets

I was asking myself, if the following list of conditions is sufficient to determine the usual smooth structure on the spaces of $k$-jets.
the map $j^k f:M\ni x\to j_x^k f\in J^k(M,N)$ is smooth, ...

**5**

votes

**0**answers

170 views

### How do metrics behave under joining along a manifold embedded in the boundary?

How do metrics behave under joining along a manifold embedded in the boundary?
This is, more-or-less, part of Problem 4.66 in Kirby's List:
Problem 4.66 How do metrics (e.g. Riemannian, Lorentz, ...

**1**

vote

**3**answers

620 views

### analytic structure on lie groups

I need a reference for a result I have heard only very vaguely "A lie group (smooth) has a compatible analytic manifold structure".
(Would even appreciate a concise way to refer to the result..)
I ...

**3**

votes

**2**answers

1k views

### A metric for Grassmannians

Hello everybody! I'm reading an article by Ricardo Mane, Hausdorff dimension
is dipheomorphism. I'm having a technical problem. Sorry for my ignorance but Would you like a
references where I can find ...

**6**

votes

**1**answer

480 views

### Surgery and homology: a reference request

I need a reference (or a short proof) for the following statement:
Suppose a closed manifold $N$ is the result of a surgery (along an embedded sphere) on a closed manifold $M$. Then the difference ...