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 Yearling
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  • 151 votes cast
Apr
26
revised Are homotopy braid groups residually nilpotent?
added 21 characters in body
Apr
16
answered Are homotopy braid groups residually nilpotent?
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?