8
votes
Accepted
Integral homology classes of which no multiples admit embedded representatives with trivial normal bundle
With the trivial normal bundle condition, it's fairly easy to produce non-realizable examples using Théorème II.2 of Thom's paper. Namely, a class $z\in H_l(M^n;\mathbb{Z})$ is realizable by an ...
6
votes
Accepted
How small need a perturbation be to not change the diffeomorphism type of a variety?
Let me prove $(1)$.
First of all, I guess that $f, \, g$ are homogeneous polynomials of the same degree $d$, otherwise $Z(f+ \varepsilon g)$ is not well-defined as a subvariety of $\mathbb{RP}^k$.
...
3
votes
Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory
The following is relatively standard. It is almost certainly not the "deep" reason you are asking for. I think it is useful point of view though.
Suppose I have some invariant $J$ which ...
2
votes
Identifying a curve on a closed surface of genus 4
As mentioned in comments, your picture is not entirely accurate. But perhaps this is what you're looking for?
(Note that, if you had chosen a different gluing pattern for your once-punctured genus-...
2
votes
Are these two natural cohomology classes of a manifold constructed from a 1-cochain and a group extension equal?
The general problem with this question is the definition of the Bockstein map. If $\widetilde G$ is non-abelian, then cochains with coefficients in $\widetilde G$ doesn't really make sense. The ...
2
votes
A Tate resolution for $\Sigma_p$ - Reference request
Your resolution is the minimal Tate complex resolving the trivial module for $\mathbb{F}_p\Sigma_p$. Each of the exterior powers of the natural permutation module is indecomposable and projective. The ...
Only top scored, non community-wiki answers of a minimum length are eligible
Related Tags
at.algebraic-topology × 7889homotopy-theory × 1704
gt.geometric-topology × 1066
ag.algebraic-geometry × 946
reference-request × 706
dg.differential-geometry × 602
ct.category-theory × 516
gn.general-topology × 506
cohomology × 504
differential-topology × 455
homological-algebra × 357
stable-homotopy × 338
kt.k-theory-and-homology × 286
simplicial-stuff × 274
gr.group-theory × 272
model-categories × 250
group-cohomology × 237
lie-groups × 223
smooth-manifolds × 222
spectral-sequences × 203
characteristic-classes × 197
homology × 190
complex-geometry × 178
higher-category-theory × 161
co.combinatorics × 154