Essays on Topology

Louis Funar (born 1967) is Directeur de Recherches at the French Centre National de la Recherche Scientifique and currently Director of the Institut Fourier, University Grenoble Alpes. His main fields of interest are geometry, topology and mathematical quantum field theory. He visited University of Pisa (1995), University of Palermo (1996-2006),  Columbia University (1996-1997), Tokyo Institute of Technology (1999-2000), IMAR Bucharest (2001, 2007), University of Ljubljana (2005, 2006), Schrodinger Institute Vienna (2013, 2014). University Babes-Bolyai (2014, 2018, 2021). He is the author of more than 80 published articles.Athanase Papadopoulos (born 1957) is Directeur de Recherche at the Centre National de la Recherche Scientifique. His main fields of interest are geometry and topology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (1984–85 and 1993–94), USC (1998–1999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019), and has had several month visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo), Presidency University (Calcutta) and Banaras Hindu University (Adjunct professor for the year 2024). He is the author of more than 200 published articles and 45 monographs and edited books on mathematics, history of mathematics, and music theory. At the University of Strasbourg, he is also member of the CREAA (Centre de Recherche et d'Expérimentation sur l'Acte Artistique).

• 1 Introduction, by Louis Funar and Athanase Papadopoulos.- 2 Primes, Knots and Po, by Barry Mazur.- 3 A short history of open manifolds related to complex analytic coordinates, by Dennis Sullivan.- 4 Universal Spin Teichmüller Theory, I: The action of P(SL(2,Z)) on T ess+, by Robert C. Penner.- 5 Universal Spin Teichmüller Theory, II: Finite presentation of P(SL(2,Z)), by Robert C. Penner.- 6 Geometry of Fermat’s sum of squares, by Greg McShane and Vlad Sergiescu.- 7 Ends and compactifications in geometric topology, by Ken’ichi Ohshika.- 8 Axiomatic phylogenetics, by Vladimir Turaev.- 9 About the diffeomorphisms of the 3-sphere and a famous theorem of Cerf (Γ4 = 0), by François Laudenbach.- 10 Holomorphic tensors on Vaisman manifolds, by Liviu Ornea and Misha Verbitsky.- 11 On the topology of monotone Lagrangians of high dimension, by Mihai Damian.- 12 Kervaire Problems in Stable Homotopy Theory, by Petr M. Akhmet’ev.- 13 Lifting generic maps to embeddings, The double point obstruction, by Sergey A. Melikhov.- 14 “Barcodes” for continuous maps and a brief introduction to Alternative Morse Theory, by Dan Burghelea.- 15 A note on the quasi simple filtration of finite groups, by Francesco Russo.- 16 Lifting maps between graphs to embeddings, by Alexey Gorelov.- 17 A note on the discriminant loci of a hypersurface of bi-degree (m, n), by Susumu Tanabé.- 18 Welded graphs, Wirtinger groups and punctured spheres, by Benjamin Audoux, Jean-Baptiste Meilhan and Akira Yasuhara.- 19 On geometric representation of L-homology classes, by Friedrich Hegenbarth and Dušan D. Repovš.- 20 On elementary invariants of genus one knots and Seifert surfaces, by Christine Lescop.- 21 On a family of hyperbolic Brunnian links and their volumes, by Dušan D. Repovš and Andrei Yu. Vesnin.- 22 SL(2, Z), les tresses à trois brins, le tore modulaire et Aut+(F2), (d’après Emil Artin et Jacob Nielsen), by Alexis Marin.- 23 “All the resources of pure mathematics”: Mathematical physics and mathematics as physics, by Arkady Plotnitsky.- 24 The case for absolute geometry, by Victor Pambuccian.- 25 The Reconstruction of Theaetetus’ Theory of Ratios of Magnitudes, by Stelios Negrepontis and Dimitrios Protopapas.- 26 Notice de travaux, by Valentin Poénaru.- 27 Mathematical Adventures: A letter to Barry Mazur, by Valentin Poénaru.- 28 Adventures in physics, by Valentin Poénaru.- 29 Dimitru Poénaru, my father, by Valentin Poénaru.- 30 Father Andrei, by Valentin Poénaru.- 31 The magic summer of 1964, by Valentin Poénaru.- 32 Po, a mathematician between humanism and science, Corrado Tanasi and Franco Marchese.