All Questions
8 questions
140
votes
7
answers
34k
views
Is the boundary $\partial S$ analogous to a derivative?
Without prethought, I mentioned in class once that the reason the symbol $\partial$
is used to represent the boundary operator in topology is
that its behavior is akin to a derivative.
But after ...
- 151k
1
vote
0
answers
131
views
Can we construct a general counterexample to support the weak whitney embedding theorm?
The weak Whitney embedding theorem states that any continuous function from an $n$-dimensional manifold to an $m$-dimensional manifold may be approximated by a smooth embedding provided $m > 2n$.
...
- 109
30
votes
2
answers
2k
views
Does there exist any non-contractible manifold with fixed point property?
Does there exist any non-trivial space (i.e not deformation retract onto a point) in $\mathbb R^n$ such that any continuous map from the space onto itself has a fixed point. I highly suspect that the ...
- 3,751
8
votes
0
answers
233
views
+300
Maps with small fibers between manifolds of equal dimension
The following question is an attempt to revise this one into what I intended.
Important revisions are shown in bold.
Are there any known examples of a compact Riemannian manifold $M$ with (possibly ...
- 491
5
votes
1
answer
282
views
Codimension zero embeddings and maps with small fibers
Edit: as explained in my comment on alesia's answer, I mistakenly did not ask below the question I intended (due to my misguided efforts to simplify it). Thus, I revised and reposted my question here.
...
- 491
5
votes
2
answers
308
views
Is this subset of matrices contractible inside the space of non-conformal matrices?
Set $\mathcal{F}:=\{ A \in \text{SL}_2(\mathbb{R}) \, | \, Ae_1 \in \operatorname{span}(e_1) \, \, \text{ and } \, \, A \, \text{ is not conformal} \,\}$, and
$\mathcal{NC}:=\{ A \in M_2(\mathbb{R}) \...
- 6,741
4
votes
0
answers
133
views
Equivalence of Flat Fiber Bundles vs Equivalence of Group Actions on the Fiber
Let's consider all flat fiber bundles with base space $B$ and fiber $F$, where $B$ and $F$ are compact and at least CW-complexes. (perhaps even topological/smooth manifolds if that helps)
All those ...
- 404
2
votes
1
answer
308
views
Does any smooth orbifold can be triangulated by orbi-simplex(triangulation of orbifolds)
every smooth manifold can be triangulated, is it true for orbifold? Is it a known result? If yes, is there any reference?
reply to the comment : G does not need to be any subgroup of Sn , any ...
- 21