arXiv subjects

Mitsunobu Tsutaya

Publications and source records attributed to Mitsunobu Tsutaya.

21 records · Page 2Linked to original sources

arXiv2014

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

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 $\mathrm{SU}(2)$-bundles over $S^4$, which is a complete classification when they are localized away from 2.

math.AT↗

arXiv2011

Finiteness of $A_n$-equivalence types of gauge groups

Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show that the number of gauge groups of principal $G$-bundles over $B$ is finite up to $A_n$-equivalence for $n<\infty$. As an example, we give a lower bound of the number of $A_n$-equivalence types of gauge groups of principal $\SU(2)$-bundles over $S^4$.

math.AT↗

arXiv2011

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

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.

math.AT↗