Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHomotopy types of gauge groups over Riemann surfaces
103
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let $G$ be a compact connected Lie group with $pi_1(G)congmathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of the moduli spaces of stable vector bundles over Riemann surfaces.
rate research
Read More
Let $M$ be an orientable, simply-connected, closed, non-spin 4-manifold and let $mathcal{G}_k(M)$ be the gauge group of the principal $G$-bundle over $M$ with second Chern class $kinmathbb{Z}$. It is known that the homotopy type of $mathcal{G}_k(M)$ is determined by the homotopy type of $mathcal{G}_k(mathbb{CP}^2)$. In this paper we investigate properties of $mathcal{G}_k(mathbb{CP}^2)$ when $G = SU(n)$ that partly classify the homotopy types of the gauge groups.
Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ and the homotopy types of the gauge groups of principal $G$-bundles over $M$ when $pi_1(M)$ is: (1)~$mathbb{Z}^{*m}$, (2)~$mathbb{Z}/p^rmathbb{Z}$, or (3)~$mathbb{Z}^{*m}*(*^n_{j=1}mathbb{Z}/p_j^{r_j}mathbb{Z})$, where $p$ and the $p_j$s are odd primes.
We determine the number of distinct fibre homotopy types for the gauge groups of principal $Sp(2)$-bundles over a closed, simply-connected four-manifold.
The $p$-local homotopy types of gauge groups of principal $G$-bundles over $S^4$ are classified when $G$ is a compact connected exceptional Lie group without $p$-torsion in homology except for $(G,p)=(mathrm{E}_7,5)$.
We construct the homotopy pullback of $A_n$-spaces and show some universal property of it. As the first application, we review the Zabrodskys result which states that for each prime $p$, there is a finite CW complex which admits an $A_{p-1}$-form but no $A_p$-form. As the second application, we investigate $A_n$-types of gauge groups. In particular, we give a new result on $A_n$-types of the gauge groups of principal $mathrm{SU}(2)$-bundles over $S^4$, which is a complete classification when they are localized away from 2.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
