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Jeremy Brazas

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My research interests include algebraic, geometric, and general topology and category theory. My most recent interests deal with generalized theories of covering spaces, topological algebra, and understanding homotopy groups of locally complicated spaces.

Research Papers:
  • J. Brazas, The unique path lifting property and generalized covering maps, Preprint, 2014. 
  • J. Brazas, P. Fabel, On fundamental groups with the quotient topology, To appear in J. Homotopy and Related Structures 2014. arXiv
  • J. Brazas, P. Fabel, Thick Spanier groups and the first shape group, To appear in Rocky Mountain J. Math. 2014. arXiv
  • J. Brazas, P. Fabel, Strongly pseudoradial spacesTopology Proc. 46 (2015) 255-276. 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.
  • 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.
Recent Talks:
  • 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: