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Abstract
This article describes recent advances in the computation of the homology groups of semialgebraic sets. It summarizes a series of papers by the author and several coauthors (P. Bürgisser, T. Krick, P. Lairez, M. Shub, and J. Tonelli-Cueto) on which a sequence of ideas and techniques were deployed to tackle the problem at increasing levels of generality. The goal is not to provide a detailed technical picture but rather to throw light on the main features of this technical picture, the complexity results obtained, and how the new algorithms fit into the landscape of existing results.
Partially supported by a GRF grant from the Research Grants Council of the Hong Kong SAR (project number CityU 11202017).
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Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong
Felipe Cucker
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Christian Albrechts University of Kiel, Kiel, Germany
Florin Manea
Durham University, Durham, UK
Barnaby Martin
Durham University, Durham, UK
Daniël Paulusma
Università degli Studi di Milano, Milan, Italy
Giuseppe Primiero
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Cucker, F. (2019). Recent Advances in the Computation of the Homology of Semialgebraic Sets. In: Manea, F., Martin, B., Paulusma, D., Primiero, G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science(), vol 11558. Springer, Cham. https://doi.org/10.1007/978-3-030-22996-2_1
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