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1

Workshop on Topology Based Methods in Data Analysis and Visualization (4th : 2011 : Zürich, Switzerland), ed. Topological methods in data analysis and visualization II: Theory, algorithms, and applications. Springer, 2012.

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2

Reyes, Mauricio, Pedro Henriques Abreu, Jaime Cardoso, et al., eds. Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87444-5.

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3

Quantum Computation with Topological Codes: From Qubit to Topological Fault-Tolerance. Springer, 2015.

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4

Lexicographical manipulations for correctly computing regular tetrahedralizations with incremental topological flipping. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1999.

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5

Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2016.

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6

Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2024.

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7

Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2024.

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8

Stanescu, Tudor D. INTRODUCTION to TOPOLOGICAL QUANTUM MATTER and QUANTUM COMPUTATION. Taylor & Francis Group, 2020.

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9

Stanescu, Tudor D. Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2016.

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10

Stanescu, Tudor D. Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2016.

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11

Stanescu, Tudor D. Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2016.

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12

Stanescu, Tudor D. Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2016.

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13

Introduction to Topological Quantum Matter and Quantum Computation. Taylor & Francis Group, 2024.

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14

Tretkoff, Paula. Topological Invariants and Differential Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0002.

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This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering
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15

Aluja, Jaime Gil, and Anna M. Gil-Lafuente. Towards an Advanced Modelling of Complex Economic Phenomena: Pretopological and Topological Uncertainty Research Tools. Springer, 2014.

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16

Aluja, Jaime Gil, and Anna M. Gil-Lafuente. Towards an Advanced Modelling of Complex Economic Phenomena: Pretopological and Topological Uncertainty Research Tools. Springer, 2012.

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17

Aluja, Jaime Gil, and Anna M. Gil-Lafuente. Towards an Advanced Modelling of Complex Economic Phenomena: Pretopological and Topological Uncertainty Research Tools. Springer, 2011.

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18

Peikert, Ronald, Hamish Carr, Helwig Hauser, and Raphael Fuchs. Topological Methods in Data Analysis and Visualization II: Theory, Algorithms, and Applications. Springer, 2016.

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19

Towards An Advanced Modelling Of Complex Economic Phenomena Pretopological And Topological Uncertainty Research Tools. Springer, 2011.

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20

Cardoso, Jaime, Mauricio Reyes, Pedro Henriques Abreu, Mustafa Hajij, and Ghada Zamzmi. Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data: 4th International Workshop, IMIMIC 2021, and 1st International Workshop, TDA4MedicalData 2021, Held in Conjunction with MICCAI 2021, Strasbourg, France, September 27, 2021, Proceedings. Springer International Publishing AG, 2021.

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21

Tu, Loring W. Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.001.0001.

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Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah–Bott and Berline–Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group actio
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