All Questions
Tagged with gauge-theory sg.symplectic-geometry
8 questions
12
votes
1
answer
522
views
Does $(S^1\times S^3)\#(S^1\times S^3)\#(S^2\times S^2)$ admit a symplectic form?
This is a crosspost from this MSE question from a year ago.
Consider the smooth four-manifold $M = (S^1\times S^3)\#(S^1\times S^3)\#(S^2\times S^2)$. Does $M$ admit a symplectic form?
If $\omega$ ...
- 19.3k
5
votes
1
answer
382
views
Stabilizer groups of Yang-Mills connections
Let $G$ be a compact Lie group with complexification $G^c$, and consider a principal $G^c$-bundle $P^c \to M$ together with a reduction $P \subseteq P^c$ to $G$. Assume that $M$ is a Riemann surface.
...
- 5,824
8
votes
1
answer
201
views
Todd genus of symplectic $4$-manifolds a smooth invariant?
Suppose that $(M_{1},\omega_{1})$ and $(M_{2},\omega_{2})$ are compact symplectic $4$-manifolds, that are (oriented) diffeomorphic. Is it true that the Todd genus ($\frac{1}{12} (c_{1}^{2} + c_{2})(M_{...
- 6,995
11
votes
1
answer
962
views
Monopole Floer Homology vs. Heegaard-Floer theory
I have a (possibly very naive) question: what is the relation between Monopole Floer Homology and Heegaard-Floer theory? (both known and conjectured)
Is there some version of Atiyah-Floer conjecture ...
- 1,981
8
votes
2
answers
591
views
Flat connections on 3-manifold with boundary
Suppose $Y$ is a 3-manifold and the boundary $\Sigma:=\partial Y$ is non-empty. Let $G$ be a Lie group with trivial center. Let $\overline {\mathcal A}_{flat}(\Sigma)$ and $\overline {\mathcal A}_{...
- 778
1
vote
1
answer
620
views
Torsion-free $G$-Structures
I have the following question. Let $G \subset SO(n)$ be a Lie Group and $M$ be a smooth manifold of dimension $n$. Furthermore let $P$ be a $G$-structure on $M$ i.e. $P$ is a principal subbundle of ...
- 25
6
votes
1
answer
520
views
Questions on R. Bryant's paper "Calibrated embeddings in the special Lagrangian and coassociative cases"
I am reading the paper "Calibrated embeddings in the special Lagrangian and coassociative cases" by R. Bryant (here the link: http://arxiv.org/abs/math/9912246) and there are certain things ...
- 63
11
votes
5
answers
1k
views
Symplectic structures from Lagrangians?
In Witten's paper 'Quantization of Chern-Simons Gauge Theory with Complex Gauge Group,' he makes the statement (p. 35) that the symplectic form on the moduli space of flat $G_\mathbb{C}$ connections ...
- 1,025