Diffeomorphism groups of Morse-Bott foliation on the solid Klein bottle by Klein bottles parallel to the boundary

• Datum: 2023
• Автори та афіліації: Sergiy Maksymenko — Institute of Mathematics of the National Academy of Science of Ukraine
• Ключові слова: keywords
• Hauptverfasser: Maksymenko, Sergiy, Максименко, Сергій
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2023
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/532
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

Let $\mathcal{G}$ be a Morse-Bott foliation on the solid Klein bottle $\mathbf{K}$ into $2$-dimensional Klein bottles parallel to the boundary and one singular circle $S^1$. Let also $S^1\widetilde{\times}S^2$ be the twisted bundle over $S^1$ which is a union of two solid Klein bottles $\mathbf{K}_0$ and $\mathbf{K}_1$ with common boundary $K$. Then the above foliation $\mathcal{G}$ on both $\mathbf{K}_0$ and $\mathbf{K}_1$ gives a foliation $\mathcal{G}'$ on $S^1\widetilde{\times}S^2$ into parallel Klein bottles and two singluar circles. The paper computes the homotopy types of groups of foliated (sending leaves to leaves) and leaf preserving diffeomorphisms for foliations $\mathcal{G}$ and $\mathcal{G}'$.