# ON THE HOMOLOGY OF THE MODULI SPACE OF $G_2$ INSTANTONS

• Park, Young-Gi (Department of Mathematics, Seoul City University, Seoul 130-743)
• Published : 1994.10.01
• 27 2

#### Abstract

Let $\pi : P \to S^4$ be a principal G-bundle over $S^4$ whose the structure group G is a compact, connected, simple Lie group. Since $\pi_3(G) = \pi_4 (BG) = Z$, we can classify the principal bundle $P_k$ over $S^4$ by the map $S^4 \to BG$ of degree k. Atiyah and Jones [2] showed that $C_k = A_k/g^b_k$ is homotopy equivalent to $\Omega^3_k G \simeq \Omega^4_k BG$ where $A_k$ is the space of the all connections in $P_k$ and $g^b_k$ is the based gauge group which consists of all base point preserving automorphisms on $P_k$. Here $\Omega^nX$ is the space of all base-point preserving continuous map from $S^n$ to X. Let $M_k$ be the space of based gauge equivalence classes of all connections in $P_k$ satisfying the Yang-Mills self-duality equations, which we call the moduli space of G instantons.