All Questions
7 questions
4
votes
1
answer
139
views
The smoothness of solutions to the Hitchin self-dual equations within a stable orbit after Sobolev completion
First, let me introduce the background of the problem: While studying chapter 4 of the Hitchin's paper "THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE", I encountered an issue. Hitchin ...
- 6,825
8
votes
0
answers
291
views
Infinitely many nonempty Seiberg-Witten moduli spaces
The classic "finiteness" statement in Seiberg-Witten (SW) theory is that, for any smooth closed connected 4-manifold, there are only finitely many spin-c structures with nontrivial SW ...
- 17.5k
2
votes
1
answer
271
views
Canonical connection on $\mathcal{A}\times X$
Let $E\rightarrow X$ be a vector bundle and let $\mathcal{A}$ denote the space of connections on $E$. Pulling back $E$ by the second projection we obtain a vector bundle $\mathbb{E}=p_2^*E\rightarrow ...
- 6,813
4
votes
1
answer
229
views
Orientability of moduli space and determinant bundle of ASD operator
Setting
In instanton gauge theory, given a $G$-principal bundle $P\to X^4$, the orientability of the moduli space of ASD connections
$$\mathcal{M}_k = \{A \in L^{2}_{k}(X, \Lambda^1 \otimes\mathrm{...
- 2,533
10
votes
2
answers
2k
views
Floer homology and Invariants for Einstein Field Equations?
Motivation: There have been the instanton (anti-self dual connection) solutions to the Yang-Mills equation $d_A^\ast F_A=0$ which extremize the YM energy $\int_M|F_A|^2$, leading to the Donaldson ...
- 17.5k
10
votes
0
answers
880
views
Central Yang-Mills connections, and flat connections with prescribed holonomy
Let $X$ be $\Sigma^g$ which is the Riemann surface of genus $g$, and consider a trivial $G$-bundle over it.
1) In this $2$-d setting, the space of Yang-Mills central connections is the set of ...
- 39.1k
11
votes
1
answer
2k
views
Seiberg-Witten theory on 4-manifolds with boundary
What generalizations of Seiberg-Witten theory to 4-manifolds with boundary do exist?
I would be especially interested in theories which "behave good" under gluing along the boundary (comparable to ...
- 27.5k