Deprecated; please use a more specific tag.

learn more… | top users | synonyms

8
votes
0answers
234 views

Can a composition with itself of a universal self-map be non-universal?

I have formulated (and published) the notion of a universal map (and of a universal morphism), and the problems below, in the early 1960-ies. DEFINITION   A continuous map   $u: ...
8
votes
0answers
461 views

Characterization of Unusual Topologies of $\mathbb R$

Following some argument over a question on math.SE, I began to wonder: We all know that in the standard topology there are no continuous bijections from $[0,1]$ to $(0,1)$ (for example by arguments ...
5
votes
0answers
527 views

Homotopy groups of a Bouquet of n-spheres

Let $$X=\vee_{\alpha\in A} S_{\alpha}^n$$ be a bouquet of $n$-spheres. Q: How does one compute the homotopy groups $\pi_k(X)$?
3
votes
0answers
183 views

A proof of the gluing axiom of a TQFT

I posted the following question on math stackexchange but I have not received any answer. So I hope people here can help me. In the book, Lectures on tensor categories and modular functors by Bakalov ...
3
votes
0answers
135 views

Topology of K3 as a sum of two abelian fibrations.

Let $E$ be a blow-up of $\mathbb{P}^2$ at 9-points in the bases locus of a pencil of elliptic curves (A $T^2$ fibration over $S^2$). K3 surfaces is obtained by removing a fiber from two copies of $E$ ...
2
votes
0answers
271 views

Bipartite Obstructions to genus $g+1$ Bipartite graph from becoming genus $g$.

Say $B_{n,n}$ is a bipartite graph on $2n$ vertices with each color assigned to $n$ vertices. Say I know $g \le genus(B_{n,n}) \le g+1$: What obstructions can $B_{n,n}$ have from becoming a genus ...
2
votes
0answers
60 views

Characterizing local homeomorphisms into an exponent

Let $X$,$Y$, and $Z$ be (compactly generated) spaces. Suppose $f:Z \to Y^X$ is a local homeomorphism. How can we tell this from its adjoint $\tilde f:Z \times X \to Y$? I.e., I want a property $P$ ...
1
vote
0answers
180 views

Good covers on complex algebraic varieties with normal crossings singularities

Let $X$ be a topological space. A good cover on $X$ is an open cover such that all finite non-empty intersections are contractible. It is a theorem of Hironaka that (complex) algebraic sets admit ...