All Questions
Tagged with loop-spaces configuration-spaces
9 questions
5
votes
1
answer
259
views
Integral homology of braid groups as a ring
Let $Br_k$ denote the braid group on $k$ strands. In Corollary A.4 of "Homology of Iterated Loop Spaces" (Page 348), Cohen-Lada-May compute $H_i(Br_k;\mathbb Z)$ as an abelian group for each ...
- 965
6
votes
1
answer
126
views
Is there a filtered splitting of product labelling spaces?
For a well-based space $X$ denote by $C(\mathbb{R};X)$ the unordered configuration space of points on the real line with labels in $X$, and a point can vanish if its label reaches the basepoint. (...
- 1,623
2
votes
1
answer
388
views
coproduct of the homology of iterated loop space on spheres
Let $\Omega^{n+1}S^{n+1}$ be the base-pointed $(n+1)$-iterated loop space on the $(n+1)$-sphere. In the paper The homology of $\mathcal{C}_{n+1}$-spaces, $n\geq 0$, F. Cohen, Lecture notes in ...
- 2,223
-2
votes
1
answer
314
views
configuration space and iterated loop space
Let the topological monoid $M$ be the configuration space $C(\mathbb{R}^n;X)=C_n(X)$ as in the book The geometry of iterated loop spaces, Theorem 5.2. I want to prove that the map $\alpha_n$ in ...
- 1,990
1
vote
0
answers
494
views
maps from labelled configuration space to section space / iterated loop space
In the paper Mapping class group and function spaces: a survey, F. Cohen, M.A. Maldonado, 2014, page 3, Section 3:
for a $m$-manifold $M$, consider the disc bundle $D(M)$ in the tangent bundle $T(M)$...
- 2,223
1
vote
1
answer
159
views
dimension of generators of cohomology ring of iterated loop-suspension
In the book The unstable Adams spectral sequence for free iterated loop spaces, R.J. Wellington, Mem. Amer. Math. Soc. 258, 1982, p. 32
Question: When $p=2$, $k\geq 1$, $n=0$ to $\infty$, what kind ...
- 2,223
1
vote
1
answer
178
views
Group completion of labelled configuration space on Euclidean spaces
In the lecture notes The Homology of $\mathcal{C}_{n+1}$-spaces, $n\geq 0$, F. Cohen, page 225 -226, it is obtained that there is a group completion on homology
$$
\alpha_n: C(\mathbb{R}^n;X)\to \...
- 2,223
0
votes
1
answer
192
views
cohomology algebra of unordered configuration space on Euclidean space
In Homology of $C_{n+1}$-spaces, $n\geq 0$, F.R. Cohen, Lecture Notes in Mathematics, Vol. 533, page 210 (the preface part before contents):
Line 2: ... is used to compute the precise algebra ...
- 1,990
0
votes
1
answer
177
views
iterated loop spaces and configuration spaces [closed]
In the lecture notes by J.P. May, The geometry of iterated loop spaces, Chapter 5, formula (1), (2) and (10), a map
$$
\phi: Hom_T(X,\Omega Y)\to Hom_T(SX,Y)
$$
is defined. And a map
$$
\eta_n=\phi^{-...
- 1,990