999 reputation
711
bio website northeastern.edu/suciu
location Boston
age
visits member for 3 years, 2 months
seen 9 hours ago

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
Jul
18
revised Is it known which links have Seifert fibered complements?
added 192 characters in body
Jul
18
answered Is it known which links have Seifert fibered complements?
Apr
3
comment Kahler structure on holomorphic principal bundles
What's a "principle" bundle?
Nov
21
comment Action of $\pi_1(S)$ on its commutator subgroup
I thought the question referred to the action of $G$ on the second derived quotient of $G$, that is, $H_1([G,G])$, rather than on the second nilpotent quotient of $G$, no?
Oct
18
revised Must the union of these two aspherical spaces be aspherical?
added reference
Oct
13
answered good reference on brieskorn manifold
Oct
1
answered Must the union of these two aspherical spaces be aspherical?
Sep
16
awarded  Yearling
Jul
29
comment On the wikipedia entry for Borel-Moore homology
Maybe there is some language confusion here, but doesn't "finite CW-complex" mean a CW-complex with finitely many cells (that is, both finite-dimensional and finite type)? So how would $X=\mathbb{Z}$ (with the discrete topology) fit in that context?
Jul
15
awarded  Informed
Jul
15
revised Cohomology of submanifold complements
added 250 characters in body
Jul
15
revised Cohomology of submanifold complements
edited body