4 papers
Thom-Milnor bounds for smooth manifolds
Saugata Basu, Antonio Lerario, Matteo Testa
We prove a smooth analogue of the classical Thom-Milnor bound, showing that the Betti numbers of the zero set of a smooth map on a compact Riemannian manifold can be controlled by…
Cohomological VC-density: Bounds and Applications
Saugata Basu, Deepam Patel
The concept of Vapnik-Chervonenkis (VC) density is pivotal across various mathematical fields, including discrete geometry, probability theory and model theory. In this paper, we i…
Complexity and speed of semi-algebraic multi-persistence
Arindam Banerjee, Saugata Basu
Let be a real closed field, a closed and bounded semi-algebraic set, and a continuous…
Equivariance in Approximation by Compact Sets
Saugata Basu, Alison Rosenblum
We adapt a construction of Gabrielov and Vorobjov for use in the symmetric case. Gabrielov and Vorobjov had developed a means by which one may replace an arbitrary set definabl…