All Questions
9 questions with no upvoted or accepted answers
15
votes
0
answers
317
views
Does there exist a closed 4-manifold whose $\pi_2$ contains torsion elements
Does there exist a closed 4-manifold $X$ such that $\pi_2(X)$ contains torsion elements?
And, if so, does there exist a closed 4-manifold $X$ such that $\pi_2(X)\neq 0$ but $\pi_2(X)\otimes \mathbb{Q}=...
- 151
14
votes
0
answers
318
views
Do Sullivan's and Wilkerson's algebraic group structures on rational homotopy automorphisms coincide?
For a 1-connected space $X$ with the homotopy type of a finite CW-complex, the homotopy automorphisms $\pi_0\,\mathrm{hAut}(X)$ are known to have the structure of an arithmetic group up to finite ...
- 8,167
6
votes
0
answers
284
views
Reference request: splittings in rational homotopy theory
It is well known that for simply-connected rational spaces,
every suspension splits as a wedge of rational spheres and
every loop space splits as a product of rational Eilenberg-Mac Lane spaces.
...
- 12.5k
5
votes
0
answers
138
views
Analog of cellular approximation theorem for $CW_0$-complexes ($CW_\mathcal P$-complexes)
$CW_0$-complexes are analogs of $CW$-complexes, in which the "building blocks" are the rational disks $D^{n+1}_0$ whose boundaries are given by $\partial D^{n+1}_0= S^n_0$, where $S^n_0$ is a ...
- 523
5
votes
0
answers
191
views
DG-Modules over CDG-algebras in the sense of rational homotopy theory
I don't know if this question is elementary or not. Suppose we have a rationalization $X_\mathbb{Q}$ of a simply connected topological space $X$. Then we can construct a CDG-algebra - a minimal ...
- 403
4
votes
0
answers
113
views
Does integration induce a Kan fibration between the mapping spaces of CDGAs and cochain complexes over $\mathbb{Q}$?
For two CDGAs $A$ and $B$ over $\mathbb{Q}$, the mapping space $\text{Map}_{CDGA}(A,B)$ is the simplicial set with $n$-simplices
$$
\Phi : A \to B \otimes \Omega^*(\Delta^n)
$$
and simplices maps ...
- 285
4
votes
0
answers
170
views
Relation between $Tor_{C^*(BG;K)}(K,K) $ and $K^G$?
Let $K$ be an algebraically closed field and $G$ a group.
Given a dg-algebra $A$, a left $A$-module $M$ and a right $A$-module $N$
let $Tor_A(M,N)$ denote the homology of the derived tensor product $M ...
- 1,361
3
votes
0
answers
79
views
Rational model for composition of linear isometries
There is a composition map on spaces of linear isometries (over $\mathbb{C}$ say)
$$
\mathcal{L}(\mathbb{C}^k, \mathbb{C}^\ell) \times \mathcal{L}(\mathbb{C}^\ell, \mathbb{C}^m) \longrightarrow \...
- 901
3
votes
0
answers
145
views
Formality of Sullivan Representatives
Suppose we have a map $f : \mathcal{A} \to \mathcal{B}$ between two formal, simply connected CDGAs, with induced map on cohomology $H(f) : H(\mathcal{A}) \to H(\mathcal{B})$. Further, suppose we have ...
- 285