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Morse homology of nonsingular Morse-Smale foliations and its duality theorem
Abstract
We define a Morse homology of the foliation which is defined by a general nonsingular Morse-Smale flow, applying the framework of the Conley index theory. In fact, we define a chain and a boundary homomorphism, therefore, a cochain and a cohomology are obtained as well. Furthermore, we prove a duality theorem on the homology and the cohomology.
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BibTeX
@misc{miyoshi2026morse,
title = {{Morse homology of nonsingular Morse-Smale foliations and its duality theorem}},
author = {Shigeaki Miyoshi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04560},
eprint = {2611.04560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04560},
}
RIS
TY - UNPB
TI - Morse homology of nonsingular Morse-Smale foliations and its duality theorem
AU - Shigeaki Miyoshi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04560
UR - https://arxiv.org/abs/2611.04560
AB - We define a Morse homology of the foliation which is defined by a general nonsingular Morse-Smale flow, applying the framework of the Conley index theory. In fact, we define a chain and a boundary homomorphism, therefore, a cochain and a cohomology are obtained as well. Furthermore, we prove a duality theorem on the homology and the cohomology.
ER -