bio | website | northeastern.edu/suciu |
---|---|---|
location | Boston | |
age | ||
visits | member for | 3 years, 2 months |
seen | 9 hours ago | |
stats | profile views | 1,463 |
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 |