Research and Publications

Jeremy Brazas




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My research interests include algebraic and general topology. More specifically, my interests deal with homotopy groups of locally complicated spaces using generalizations of covering space theory and topological algebra.

Research Papers:
  • J. Brazas, H. Fischer, Test map characterizations of local properties of fundamental groups. Preprint. 2017. arXiv
  • J. Brazas, Generalized covering space theories, Theory and Appl. of Categories 30 (2015) 1132-1162. pdf
  • J. Brazas, P. Fabel, On fundamental groups with the quotient topology, J. Homotopy and Related Structures 10 (2015) 71-91. arXiv
  • J. Brazas, P. Fabel, Strongly pseudoradial spacesTopology Proc. 46 (2015) 255-276. arXiv
  • J. Brazas, P. Fabel, Thick Spanier groups and the first shape group, Rocky Mountain J. Math. 44 (2014) 1415-1444. arXiv
  • J. Brazas, Open subgroups of free topological groups, Fundamenta Mathematicae 226 (2014) 17-40. arXiv
  • J. Brazas, Semicoverings, coverings, overlays and open subgroups of the quasitopological fundamental group, Topology Proc. 44 (2014) 285-313.
  • J. Brazas, The fundamental group as a topological groupTopology Appl. 160 (2013) 170-188. arXiv
  • J. Brazas, Semicoverings: a generalization of covering space theory, Homology Homotopy Appl. 14 (2012) 33-63. pdf
  • J. Brazas, The topological fundamental group and free topological groups, Topology Appl. 158 (2011) 779-802. arXiv
Math Education/Popular Math Papers:
  • T. Abel, J. Brazas, Pedagogically Inconvenient Functions for Teaching Transformations, The College Mathematics Journal, Vol 47, No. 3, (May 2016), pp. 200-206.
  • T. Abel, J. Brazas, Developing Digital Literacy in the Calculus Sequence, To appear in the Proceedings of the International Conference on Technology in Collegiate Mathematics, 2016.
  • J. Brazas, D. Priest, Using the floor function to prove the countability of the rationals, AMATYC Review 29 no. 2, 2008.
Undergraduate Research Projects Advised:
  • Luis Matos: The coarse Hawaiian earring: a countable space with uncountable fundametnal group. 2014-2015
    • Click HERE for the pdf.
    • This paper is the result of research completed as part of the RIMMES program 2014-2015.
  • Sean Keeler: Finite Topological Spaces from a Categorical Perspective. 2016-2017
Selected Conference Talks:
  • Developing Digital Literacy in the Calculus Sequence (Joint with Todd Abel), 28th International Conference on Technology in Collegiate Mathematics, Atlanta, GA. March 12, 2016.
  • A characterization of the unique path lifting property for the whisker topology, Joint Meeting of the German and Polish Mathematical Societies (DMV-PTM), Invited talk in Wild Algebraic & Geometric Topology session, Poznan, Poland, September 18, 2014. Slides
  • Topological fundamental groups and open subgroup theorems, Lloyd Roeling Lafayette Mathematics Conference, Invited talk, UL Lafayette, November 9, 2013.
  • Quasitopological fundamental groups and the first shape map, 28th Summer Conference on Topology and Its Applications, Invited talk in Continuum Theory Session, Nippissing University, July 26, 2013. Abstract   Slides
  • Open subgroups of free topological groups, 47th Spring Topology and Dynamics Conference, Central Connecticut State University, March 24, 2013. Abstract   Slides
Ph.D. Dissertation:
  • J. Brazas, Homotopy Mapping Spaces, University of New Hampshire Ph.D. Dissertation, 2011.
Miscellaneous notes: