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9 votes
2 answers
622 views

Can we foliate the punctured space by tori?

Is it possible to have a 2 dimensional foliation of $\mathbb{R}^{3}-\{0\}$ such that each leaf is homeomorphic to the torus? what algebraic topological obstruction exist? Another question: is there ...
Ali Taghavi's user avatar
3 votes
1 answer
246 views

Borel-Moore homology for resolution of singularities

Let $X$ be a singular projective variety. Denote by $Z$ the singular locus of $X$. Consider the resolution of singularities $$\pi: \widetilde{X} \to X$$ Denote by $E$ the exceptional divisor. We know ...
user45397's user avatar
  • 2,323
1 vote
0 answers
126 views

Blow up of simply connected isolated singularity

Let $X \subset \mathbb{C}^n$ be a simply connected complex variety with a unique isolated singularity at $x\in X$. Let $\tilde{X}$ be the strict transform of $X$ under the blow-up $\mathrm{Bl}_x(\...
Serge the Toaster's user avatar