The Net Advance of Physics:
TOPOLOGY

: TOPOLOGY: (under construction)

• General:
  • Set theory and topology. An introduction to the foundations of analysis. Part I: Sets, relations, numbers by Felix Nagel [2013/06] 152 pp.
  • Topologies and all that -- A Tutorial by Ernst-Erich Doberkat [2015/03]
  • Use of topology in physical problems by Somendra M. Bhattacharjee [2015/12]
  • Point-set topology by F. Shahi [2022/02] 288 pp.

• Type: ALGEBRAIC:
  • Algebraic Topology by Vanessa Robins [2013/04]
  • Signatures [of quadratic forms] in algebra, topology and dynamics by Etienne Ghys and Andrew Ranicki [Ensaios Matematicos 30, 1 (2016)] 173 pp.
  • Persistent topology for natural data analysis: a survey by Massimo Ferri [2017/06]
  • A Brief History of Persistence by Jose A. Perea [2018/09] Persistent homology.
  • Goodwillie Calculus by Gregory Arone and Michael Ching [2019/02]
  • A Factorization Homology Primer by David Ayala and John Francis [2019/03]
  • Topological Persistence [Modules] in Geometry and Analysis by Leonid Polterovich et al. [2019/04] 136 pp.
  • Homological stability: A tool for computations by N. Wahl [2022/03]

• Type: ARITHMETIC:
  • [Open] Problems in Arithmetic Topology by C. Gómez-Gonzáles and J. Wolfson [2020/12]

• Type: COMPUTATIONAL:
  • Persistent topology for natural data analysis: a survey by Massimo Ferri [2017/06]
  • The importance of the whole: topological data analysis for the network neuroscientist by Ann E. Sizemore et al. [2018/06]
  • Computational and Applied Topology Tutorial by Paweł Dłotko [2018/07]

• Type: DIFFERENTIAL:
  • Lectures on Differential Topology by Riccardo Benedetti [2019/07] 416 pp.

• Type: GEOMETRIC:
  • An Introduction to Geometric Topology by Bruno Martelli [2016/10] 482 pp.
  • An invitation to higher Teichmüller theory by Anna Wienhard [2018/03]
  • Lecture Notes on CAT(0) Cube Complexes by Petra Schwer [2019/10]

• Type: NON-COMMUTATIVE:
  • A Case Study in Non-Commutative Topology [irrational rotation C* algebra] by Claude L. Schochet [2017/11]

• Type: POINTFREE:
  • Pointfree topology and constructive mathematics by G. Manuell [2023/04]

• Type: STATISTICAL/STOCHASTIC:
  • Concepts of polymer statistical topology by S. K. Nekchaev [2015]
  • Random simplicial complexes by Matthew Kahle [2016/07]

• Aspects: DILATATION:
  • Une invitation aux surfaces de dilatation by Selim Ghazouani [2019/01]

• Aspects: KOLGOMOROV QUOTIENTS:
  • A Survey of Kolgomorov Quotients by Teemu Pirttimäki [2019/05]

• Aspects: FIXED POINTS:
  • Reflections in a cup of coffee [Brouwer's Fixed Point Theorem] by Raf Bocklandt [2016/12]

• Aspects: POINCARE-HOPF THEOREM:
  • O Teorema de Poincare-Hopf by Jean-Paul Brasselet and Nguyen Thi Bich Thuy [2017/10]

• Re: CHIRALITY:
  • Chirality: A Scientific Leitmotif by F. Wilczek [2021/12]

• Re: CRYSTALS:
  • Topology in Abundance by Étienne Lantagne-Hurtubise and Marcel Franz [Nature Reviews Physics 1, 183 (2019)]

• Re: NEUROSCIENCE:
  • The importance of the whole: topological data analysis for the network neuroscientist by Ann E. Sizemore et al. [2018/06]

• Re: QUASICRYSTALS:
  • Topology in quasicrystals by O. Zilberberg [2020/12]

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