#### 49 Citations

Poincaré’s stated motivations for topology

- Computer Science
- 2020

This paper examines carefully the stated motivations of Poincaré and potential applications he had in mind for developing topology and sheds some light on the broad interest of PoINCaré in mathematics in a concrete way. Expand

Poincaré’s Geometric Worldview and Philosophy

- Philosophy
- Geometry in History
- 2019

Poincare is one of the pioneers in non-Euclidean geometry and topology. In this paper, we shall first review his work on non-Euclidean geometry and topology. Then we shall see how his researches in… Expand

Topology of Singular Spaces: Motivation, Overview

- Mathematics
- Graduate Texts in Mathematics
- 2019

In this chapter, we overview the main results and properties of the (co)homology of manifolds, and show in examples that these results fail to be true for singular spaces. This motivates the use of… Expand

Analogy and Invention Some Remarks on Poincaré’s Analysis Situs Papers

- Mathematics
- 2018

The primary role played by analogy in Henri Poincare’s work, and in particular in his “analysis situs” papers, is emphasized. Poincare’s “sixth example” (showing that Betti numbers do not suffice to… Expand

The Surprising Resolution of the Poincaré Conjecture

- Mathematics
- 2018

In 2003, Grigory Perelman proved the celebrated Poincare conjecture, establishing that the simplest topological property (simple-connectivity) characterizes the simplest closed three-manifold (the… Expand

The Homology and Cohomology Theories

- Mathematics
- 2016

It is not clear from the initial definitions of Poincare that the Betti numbers of a compact manifold are finite or that its fundamental group is finitely generated. In order to address in particular… Expand

Computing and analyzing recoverable supports for sparse reconstruction

- Mathematics, Computer Science
- Adv. Comput. Math.
- 2015

This work considers the case of large k and introduces a method which constructs vectors which support has the cardinality k and which can be recovered via ℓ1 minimization and proposes a methodology to quickly check whether a given vector is recoverable. Expand

A novel technique for cohomology computations in engineering practice

- Computer Science
- 2013

This paper introduces a novel technique to effectively compute cohomology generators focusing on the application involving the potential definition for h-oriented eddy-current formulations, which is completely automatic, computationally efficient and general. Expand

Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

- Computer Science
- Comput. Phys. Commun.
- 2013

This algorithm solves one of the most long- lasting problems in low-frequency computational electromagnetics, when generators are employed in the physical modeling of magneto-quasistatic problems, allowing to handle problems not addressable before. Expand

The Conley index, gauge theory, and triangulations

- Mathematics
- 2013

This is an expository paper about Seiberg–Witten Floer stable homotopy types.We outline their construction, which is based on the Conley index and finite-dimensional approximation. We then describe… Expand