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
Math Education/Popular Math
- 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.
- 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 spaces, Topology
Proc. 46 (2015) 255-276. arXiv
- J. Brazas, P. Fabel, Thick
groups and the first shape group, Rocky Mountain J. Math. 44
(2014) 1415-1444. arXiv
- J. Brazas, Open
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
as a topological group, Topology
Appl. 160 (2013) 170-188. arXiv
- J. Brazas, Semicoverings:
generalization of covering space theory,
Homology Homotopy Appl.
(2012) 33-63. pdf
- J. Brazas, The
fundamental group and free topological
groups, Topology Appl. 158
(2011) 779-802. arXiv
Undergraduate Research Projects
- T. Abel, J. Brazas, Pedagogically
Inconvenient Functions for Teaching Transformations, The
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
- J. Brazas, D. Priest, Using
the floor function to prove the countability of the rationals, AMATYC
Review 29 no. 2, 2008.
Selected Conference Talks:
- Luis Matos: The
coarse Hawaiian earring: a countable space with uncountable fundametnal
- 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
- Developing Digital
Literacy in the Calculus Sequence (Joint with Todd Abel), 28th
International Conference on Technology in Collegiate Mathematics,
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.
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
- Open subgroups of free
topological groups, 47th
Spring Topology and Dynamics Conference, Central Connecticut State
University, March 24, 2013. Abstract
- J. Brazas, Homotopy
Spaces, University of New
Hampshire Ph.D. Dissertation, 2011.