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### Does anyone know how to describe the zero set of the Jacobian of injective harmonic maps in space?

For example consider the following question:
Let $\mathbb{B}^m$ be hyperbolic space and let $f
: \mathbb{B}^m \rightarrow \mathbb{B}^m$ be harmonic $K$-qc map.
Whether $f$ has critical points on ...

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### How to rewrite this logarithmic update rule [closed]

I tried to rewrite the equation given below. I get stuck getting rid of the $ P(n|z_{1:t})$ on the left side. How can this be done?
$$
P(n|z_{1:t}) = \left[1+ \frac{1-P(n|z_{t})}{P(n|z_t)} ...

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277 views

### When is the inclusion of a relative mapping space into a mapping space a cofibration?

Let $(X,A)$ and $(Y,B)$ be pairs of spaces and subspaces, let $\operatorname{Map}(X,Y)$ the space of maps $f:X\to Y$ equipped with the compact-open topology and let $\operatorname{Map}(X,A;Y,B)$ be ...

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### Whitehead product with identity on homotopy groups of spheres

For $n\geq 2$ let $(S^n,p)$ be the $n$-sphere with a base point $p$. Let $1:S^n\to S^n$ denote the identity map. Let us define the map
$Wh_1: \pi_i(S^n,p)\to \pi_{i+n-1}(S^n,p), \alpha\mapsto ...

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972 views

### Induced map on path manifolds: is it a submersion?

Consider the following claim:
Let $p:M \to N$ be a (surjective) submersion of finite-dimensional smooth
manifolds. Let $J$ denote one of $[0,1],\ [0,1),\ (0,1]$. Then $p_*:M^J \to
N^J$ is a ...

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509 views

### Remap FFT frequency bin distribution

I've coded up the FFT for a dataset I'm working with. My intent is to create a waterfall plot of the result, but the problem I'm running into is if I change my input data size, then I get a different ...

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### Is there a manifold structure on a space of conformal maps?

I would be very grateful for any information or pointers for the following:
1) Fix an open subset $U$ of $\mathbb{CP}^1$. a) Does the set of all holomorphic maps from $U$ to $\mathbb{C}$ (with the ...

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154 views

### Contractible space of maps between Eilenberg-Mac Lane spaces, 2

Let $G$ and $H$ be torsion abelian groups.
Are the following are equivalent:
$\mathrm{Hom}(G, H) = 0$
$\mathrm{map}_*( K(G, m), K(H,n)) \sim *$ for all $n, m\geq 1$
?
Clearly (2) implies (1).

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293 views

### Contractible space of maps between Eilenberg-Mac Lane spaces

Suppose $A$ is an abelian torsion group, with no elements of order $p$, and let
$P$ be an abelian $p$-group (i.e., the order of each element is a power of $p$).
It sure seems to me that
$$
...

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299 views

### The Space of Cellular Maps

Let $X$ and $Y$ be CW complexes.
Inside of the space of maps $\mathrm{map}(X,Y)$, we have the subspace $\mathrm{CW}(X,Y)$, consisting of just the cellular maps from $X$ to $Y$. The Cellular ...