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Sep
16 |
awarded | Yearling |
Mar
20 |
comment |
cohomology ring of configuration spaces
Link is dead... |
Jan
16 |
comment |
Relation between Milnor fiber and its restriction via vanishing cycles
I recommend scholar.google.com |
Jan
13 |
comment |
Smooth 4-manifolds with $E_8$ intersection form
@AlexDegtyarev: The Enriques surface has intersection form $E_8\oplus U$, not $2U$. Indeed, its second Betti number is 10, since $b_1=0$, and the Euler characteristic is 1/2 the Euler characteristic of the K3 surface. |
Dec
13 |
awarded | Necromancer |
Dec
10 |
answered | Fundamental groups of normal complex quasi-projective varieties |
Dec
7 |
comment |
Can any Delone set be approximated by a model set?
The Delaunay triangulation is almost universally spelled that way, as in the original French form of the name, instead of the Cyrillic transliteration... |
Dec
7 |
comment |
Can any Delone set be approximated by a model set?
Is Delone an alternate spelling of Boris Delaunay (en.wikipedia.org/wiki/Boris_Delaunay), or is that someone else? |
Dec
7 |
comment |
Lower Central Series of Pure Braid Groups?
Have you tried looking at the book on Combinatorial group theory by Magnus, Karrass, and Solitar? |
Dec
7 |
comment |
Lower Central Series of Pure Braid Groups?
By induction on $n$, using the known structure of $\Gamma_k F_r$. |
Dec
7 |
answered | Lower Central Series of Pure Braid Groups? |
Nov
28 |
comment |
Action of the pure braid group on the commutator subgroup of a free group
For a thorough discussion of the status of the faithfulness problem for the Gassner representation, see Joan Birman's review of the paper "Braid groups are linear groups" by Seymour Bachmuth, at ams.org/mathscinet-getitem?mr=1399602 |
Nov
2 |
comment |
Bockstein homomorphism from $H^d(BG,Z_2)$ to $H^{d+1}(BG,Z)$, and Steenrod Square $Sq^1$
Yes, that's correct. |
Oct
31 |
comment |
How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?
@FernandoMuro: the group ring $\mathbb{Z} G$ of a group $G$ is the free abelian group on $G$ (as a group). |
Oct
30 |
comment |
How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?
The second homotopy group of $M\# N$ is the group ring of $\pi_1(M)*\pi_1(N)$. Composing with the Hopf map $S^3\to S^2$ yields non-trivial elements of $\pi_3(M\# N)$. When, say, $M$ is a lens space, we also have non-trivial elements of $\pi_3(M\# N)$ coming from $\pi_3(M)=\mathbb{Z}$. |
Sep
16 |
awarded | Yearling |
Aug
7 |
comment |
Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Yes, $H_2$ of an fp group is finitely generated. But, say, $H_3$ needs not be finitely generated. The first such example was given by John Stallings, in a seminal paper, titled, sure enough, A finitely presented group whose 3-dimensional integral homology is not finitely generated, see here. |
Aug
7 |
comment |
Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Also, "infinite homology" means "infinite-dimensional homology" (as $\mathbb{Q}$-vector space), right? |
Aug
7 |
comment |
Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Just to make sure: the assertion that $H_i(G,\mathbb{Q})$ is finite-dimensional (for all $i>2$) is an assumption, yes? |
Jul
19 |
awarded | Nice Answer |