Questions tagged [rational-homotopy-theory]
The rational-homotopy-theory tag has no usage guidance.
111 questions
2
votes
1
answer
159
views
natural co-product on minimal Sullivan model
Let M be a compact manifold. The diagonal $M \rightarrow M \times M$ induces
co-product on singular cohomolgy $H^*(M) \rightarrow H^*(M) \times H^*(M)$ via Poincare duality.
I would like to know if ...
- 745
2
votes
0
answers
120
views
Homotopy groups of homotopy fixed points of a $\mathbb{Z}\left[\frac{1}{\lvert G\rvert}\right]$-local orthogonal spectrum
Let $G$ be a finite group and $X$ an orthogonal $\mathbb{Z}\left[\frac{1}{\lvert G\rvert}\right]$-local spectrum with an $G$-action that is trivial on $\pi_*X$.
I want to show that then the map $X^{hG}...
- 21
2
votes
0
answers
170
views
Geometric fixed points of induction spectrum
I was reading the paper "The Balmer spectrum of rational equivariant cohomology theories" of J.P.C. Greenlees and I found the following interesting fact, expressed in Lemma 4.2 and Remark 4....
- 767
2
votes
0
answers
58
views
Projective resolution of a dual coefficient system
I was trying to read the paper "Equivariant minimal models" by G. Triantafillou(1982) and was trying to compute cohomology of a system of DGA with rational coefficient system. Given a finite ...
- 1,177
2
votes
0
answers
320
views
Homology of homotopy fiber of inclusion
We consider an inclusion $j: A \hookrightarrow X$. Let $A_j = A \times_X PX$ be the homotopy fiber (which is the fiber of the fibration associated to $j$). The space $PX$ there is the Moore path space ...
- 21
1
vote
0
answers
162
views
Can formality be read from the cohomology algebra
A cgda $(A,d)$ is formal if it is weakly equivalent to $(H(A),0)$. There are several equivalent conditions for this. Similarly, a space $X$ is formal if the cgda $(A_{PL}(X),d)$ of polynomial ...
- 1,452
1
vote
0
answers
46
views
A question related to injective envelope for a system of DGA's
I was trying to read Fine and Triantafillou's paper "On the equivariant formality of Kahler manifolds with finite group action".
They have defined the enlargement at $H$ of a system of DGA's ...
- 1,177
1
vote
0
answers
127
views
PD model for CDGA over the integers
Lambrechts and Stanley constructed Poincaré duality model for cdga over a field with simply connected cohomology. Are there construction of PD model for CDGA over integer coefficients?
- 745
1
vote
0
answers
409
views
Rational homotopy and l-adic cohomology
In rational homotopy theory there is a basic construction which, given a prime number $l$ and a $CW$-complex $X$, produces a localized space $X_l$ equipped with a map $X\rightarrow X_l$ that induces ...
user95283
0
votes
1
answer
174
views
Compute the rational cohomology ring $H^*(M;\mathbb{Q})$ of a product of Lie groups (and their quotients)
As the following product is a bit unfamiliar to me:
How do we compute the rational cohomology ring $H^*(M;\mathbb{Q})$ of the product of Lie groups:
$M=SO(n_1)\times U(n_2)\times SU(n_3)\times (...
- 239
-5
votes
1
answer
409
views
Computing $H^*(BDiff(W_{\infty},D^{\infty});\mathbb{Q})$ via Mumford-Morita-Miller classes
Galatius and Randal-Williams proved the following generalized Mumford conjecture in their joint paper, "Stable Moduli spaces of High Dimensional Manifolds". For each characteristic class of oriented $...
- 239