Ryuma Orita
Tokyo Journal of Mathematics, vol. 48 (2025), no. 1, pp. 217-230
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Overview#
How many continuous rules are needed to choose a path between any two points of a space? Farber’s topological complexity measures this aspect of motion planning. This paper asks how the symplectic geometry of a manifold constrains that number.
We study closed, four-dimensional spherically monotone symplectic manifolds whose Kodaira dimension is not $-\infty$. For this class, we obtain estimates for topological complexity, connecting a question about motion planning with the geometry and topology of symplectic four-manifolds.
BibTeX
@article{orita2025topological,
author = {Orita, Ryuma},
title = {{Topological complexity of monotone symplectic manifolds}},
journal = {Tokyo Journal of Mathematics},
volume = {48},
number = {1},
pages = {217--230},
year = {2025},
doi = {10.3836/tjm/1502179420},
eprint = {2311.14989},
archivePrefix = {arXiv}
}