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13 votes
3 answers
2k views

When does homology represent an embedded sphere?

If we have a triangulation of a manifold $M$ of dimension $i$ and we have simplicial homology $H_i(M)=\mathbb{Z}$, what is the condition than there exists an embedded sphere $S^i$ that generates the ...
Jake B.'s user avatar
  • 1,465
1 vote
1 answer
116 views

On graph imbedding genus clarification

Given a graph the minimum genus $g$ is the minimum number of handles needed so that there an imbedding of the graph on the surface with no edge crossings. If the graph is of genus $g$ then is there ...
Turbo's user avatar
  • 13.9k
4 votes
0 answers
69 views

Obstructions to symplectically embedding compact manifolds of dimension $4$ or higher

It is known in Li's paper (http://arxiv.org/pdf/0812.4929v1.pdf) that in compact symplectic manifolds $(X^{2n},\omega)$ of dimension at least $2n\geq 4$, an immersed symplectic surface represents a $2$...
Sinister Cutlass's user avatar