Event
01_1
| 제출번호(No.) | 0048 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Topology (TO) |
| 영문제목 (Title(Eng.)) |
Maximal holonomy of infra-Nilmanifolds with $\mathcal{H}_7(\mathbb{H})$-geometry |
| 저자(Author(s)) |
Daehwan Koo1, Joonkook Shin2 Daejeon Science High School for the Gifted1, Chungnam National University2 |
| 초록본문(Abstract) | In this talk, we study the special Lie group which is called the twisted quaternionic Heisenberg group $\mathcal{H}_7(\mathbb{H}) = \mathbb{R}^3 \tilde\times \mathbb{R}^4$. It is a 7-dimensional nilpotent Lie group with group operation $ (s, \mathbf{x})(t,\mathbf{y}) = (s+t+2\mathcal{I}(\mathbf{x},\mathbf{y}), \mathbf{x}+\mathbf{y}).$ Our aim is to study the 7-dimensional infra-nilmanifolds modeled on $\mathcal{H}_7(\mathbb{H})$ and investigate the maximal order of their holonomy group. First we show that $ \mathrm{Aut}(\mathbb{R}^3 \tilde\times \mathbb{R}^4) \cong \mathrm{Hom}(\mathbb{R}^4, \mathbb{R}^3) \rtimes O(\mathbf{J};2,2)$, where $O(\mathbf{J};2,2) = SO_0(2,2) \times \mathbb{R}^+$. Then we prove that there exists an almost Bieberbach group $\varPi \subset \mathcal{H}_7(\mathbb{H})\rtimes\mathrm{Aut}(\mathcal{H}_7(\mathbb{H}))$ whose maximal holonomy group has order $36$. |
| 분류기호 (MSC number(s)) |
20H15, 20F18, 20E99, 53C29 |
| 키워드(Keyword(s)) | almost Bieberbach group, holonomy group, infra-nilmanifold |
| 강연 형태 (Language of Session (Talk)) |
Korean |