# Questions tagged [mapping-space]

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20
questions

**3**

votes

**1**answer

212 views

### Conformal map onto a circle, from an identification space composed of five squares

I am looking to derive a conformal map for the problem illustrated in this image. I've read a bit about how to map a square onto a circle, but I'm struggling to extend the concepts for the domain at ...

**2**

votes

**0**answers

45 views

### Stability for mapping class groups, spaces of sections, and polynomial coefficient systems

Let $X$ be a simply connected space. Cohen and Madsen https://arxiv.org/abs/math/0601750 proved that the functor sending a surface with boundary M to $H_i(Map(M,X))$ has polynomial degree $\leq i$. ...

**2**

votes

**1**answer

104 views

### Do submersions induce open maps between spaces of differentiable maps?

Let $X$, $Y$ and $Z$ be smooth manifolds.
Any differentiable map $f \colon Y \rightarrow Z$ induces a continuous map $f_{\ast} \colon C^{\infty}(X, Y) \rightarrow C^{\infty}(X, Z)$ via composition $g \...

**2**

votes

**0**answers

51 views

### Simplicial models for mapping spaces of filtered maps

Let $S$ and $K$ be simplicial sets with $K$ Kan. Given simplicial sets $S$ and $K$, we let $SIMP(S,K)$ be the internal hom in the category of simplicial sets. Hence $SIMP(S,K)$ is Kan.
Suppose that ${...

**-1**

votes

**1**answer

75 views

### Hierarchies of Operator Norms [closed]

Given some linear operator $T: V \mapsto W$, we can talk about the operator norm between the spaces V and W, i.e.
$$
\| T \|_{V \mapsto W} \ = \ \sup_{g} \| Tg \|_W \ , \quad \mbox{ with } \| g \|_V \...

**3**

votes

**1**answer

213 views

### Morphisms of parametrized ring spectra

This is a follow-up to this question, in which Denis Nardin nicely explained that
$$
\operatorname{Map}_{\operatorname{Fun}(X, \operatorname{Sp})}(E_X, E'_X)
\simeq
\operatorname{Map}(X, \operatorname{...

**2**

votes

**1**answer

152 views

### Are morphisms of parametrized spectra themselves parametrized morphisms of spectra?

Let $X$ be a fixed parametrizing space. Let $E$ and $E'$ be two spectra and let $E_X$ and $E'_X$ be their trivial parametrized versions. Intuitively I imagine that the morphisms of parametrized ...

**0**

votes

**1**answer

2k views

### Is the Haversine Formula or the Vincenty's Formula better for calculating distance?

Which is better for calculating the distance between two latitude/longitude points, The Haversine Formula or The Vincenty's Formula? Why?
The distance is obviously being calculated on Earth. Does ...

**5**

votes

**1**answer

223 views

### Homotopy Type of the Based Mapping Space $Map_*^{(k,l)}(\mathbb{C}P^2,BU(2))$

Path components of the based mapping space $Map_*(\mathbb{C}P^2,BU(2))$ are indexed by a pair of integers $(k,l)$ determined by the values of the first two Chern classes that a map $f:\mathbb{C}P^2\...

**4**

votes

**1**answer

116 views

### Homotopy equivalence of maps with compact support and maps which vanish at infinity

Let $X$ be a nice space, maybe a manifold, and let $Y$ be a based space.
What sort of conditions must we impose on $Y$ (and $X$ if need be) to get a homotopy equivalence
$$
\mathcal C_c(X,Y) \simeq \...

**8**

votes

**1**answer

563 views

### cohomology of iterated loop space on spheres

In the book The homology of iterated loop spaces, the homology Hopf algebra
(1)
$$
H_*(\Omega^n \Sigma^n X;\mathbb{Z}_p)
$$
for primes $p\geq 2$ is obtained on p. 226, Thm. 3.2. In particular, the ...

**2**

votes

**0**answers

170 views

### cohomology ring of mapping spaces

In the lecture notes The homology of $\mathcal{C}_{n+1}$–spaces, n ≥ 0. F. Cohen, 1978, page 228-231, the cohomology ring
$$
H^*(\text{Map}_*(S^n, S^n\wedge X);\mathbb{Z}_p)
$$
is obtained for any ...

**2**

votes

**1**answer

480 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 ...

**17**

votes

**1**answer

1k views

### 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 [\...

**11**

votes

**3**answers

1k 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 ...

**0**

votes

**1**answer

689 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 ...

**7**

votes

**1**answer

2k views

### 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 ...

**4**

votes

**1**answer

180 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).

**4**

votes

**1**answer

373 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
$$
\mathrm{...

**6**

votes

**0**answers

340 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 ...