Questions tagged [mapping-space]
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10
questions with no upvoted or accepted answers
9
votes
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answer
619
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Does the continuous mapping space between topological manifolds always admit a Banach manifold structure?
Let $M$ and $N$ be smooth, i.e. $C^\infty$, manifolds. Suppose that $M$ is compact. Then for every $k \geq 0$ it is well known that $$C^k(M,N)$$ admits the structure of a smooth Banach manifold. I am ...
- 518
6
votes
0
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358
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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 ...
- 12.5k
3
votes
0
answers
215
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Confused about the definition of the Kahn-Priddy map
The Kahn-Priddy map is defined in various papers as follows:
Define $i:\mathbb {RP}^{n-1}\rightarrow O(n)$ by taking $\ell\in \mathbb {RP}^{n-1}$ to the reflection across $\ell^\perp.$ Define $j:O(n)\...
- 1,175
3
votes
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65
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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 $\leq i$. ...
- 925
2
votes
0
answers
127
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Quantifierisation of maps
I will rewrite my question using Matt F. suggestion.
Consider the logical structure $L = (\mathbb{R}, +, *, 1, 0, =)$ and a function $f:\mathbb{R}\to\mathbb{R}$.
Consider the map $Q:2^\mathbb{R}→2^\...
- 319
2
votes
0
answers
54
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 ${...
2
votes
0
answers
195
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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 ...
- 2,213
0
votes
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202
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Mapping between pseudosphere and breather segments
The pseudospheres $(K=-1)$ shown contain two cuspidal edge boundaries and appear to admit isometric mapping between 1) the surface of revolution through an expansion/contraction deformation in ...
- 907
0
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0
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89
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Topologies in $\mathcal{C}^\infty(M,N)$
Naively, one could topologise the set of smooth (ie $\mathcal{C}^\infty$) maps between two smooth manifolds $M \to N$ with the subspace topology $\mathcal{C}^\infty(M,N) \subseteq \mathcal{C}^0(M,N)$, ...
- 571
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Can we construct a surjective mapping from $\mathbb{R}^{?}$ to this space?
(Note : I'm not sure about the tags, please re-tag this if you think you have the right tag).
I am optimising a certain function over a certain space (that i will describe), and to use non-constraint ...
- 686