Homotopy pullback of $A_n$-spaces and its applications to $A_n$-types of gauge groups

Mitsunobu Tsutaya

paper

Homotopy pullback of $A_{n}$ -spaces and its applications to $A_{n}$ -types of gauge groups

arXiv:1210.8252

Abstract

We construct the homotopy pullback of $A_{n}$ -spaces and show some universal property of it. As the first application, we review the Zabrodsky's 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 $SU (2)$ -bundles over $S^{4}$ , which is a complete classification when they are localized away from 2.

24 pages, made many corrections, separated Section 8 into Section 8 and 9

References in corpus (1)

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

Homotopy pullback of An​-spaces and its applications to An​-types of gauge groups

Abstract

References in corpus (1)

Homotopy pullback of $A_{n}$ -spaces and its applications to $A_{n}$ -types of gauge groups