Non-singular extensions of circle-valued Morse functions

Koki Iwakura

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arXiv · 2311.07309

Non-singular extensions of circle-valued Morse functions

Koki Iwakura

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Abstract

In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular extension of a circle-valued Morse function as the main theorem when a submersion on a collar neighborhood is given.

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Koki Iwakura. 2023-11-13. Non-singular extensions of circle-valued Morse functions. https://arxiv.org/abs/2311.07309

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