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math.GT2026
Morse complexity of homology classes
Fedor Manin, Bena Tshishiku, Shmuel Weinberger
The Morse complexity of a manifold is the minimal number of handles required to build it. We explore the Morse complexity of manifolds, bordisms, and homology classes, proving nont…
math.GT2026
Quantitative PL bordism
Fedor Manin, Bena Tshishiku, Shmuel Weinberger
We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as well as various more exotic theories such as…
math.GT2024
On Freedman's link packings
Fedor Manin, Elia Portnoy
Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on…