A note on homotopy types of connected components of Map(S^4,BSU(2))

Mitsunobu Tsutaya

doi:10.1016/j.jpaa.2011.10.020

paper

A note on homotopy types of connected components of Map(S^4,BSU(2))

arXiv:1101.4278 · doi:10.1016/j.jpaa.2011.10.020

Abstract

Connected components of $\Map(S^4,B\SU(2))$ are the classifying spaces of gauge groups of principal $\SU(2)$-bundles over $S^{4}$ . Tsukuda [Tsu01] has investigated the homotopy types of connected components of $\Map(S^4,B\SU(2))$. But unfortunately, the proof of Lemma 2.4 in [Tsu01] is not correct for $p = 2$ . In this paper, we give a complete proof. Moreover, we investigate the further divisibility of $ε_{i}$ defined in [Tsu01]. In [Tsu], it is shown that divisibility of $ε_{i}$ have some information about $A_{i}$ -equivalence types of the gauge groups.

References in corpus (1)

Finiteness of $A_{n}$ -equivalence types of gauge groups