Keywords
Fundamental Group
Group Action
How to Cite
Abstract
In 1966, F. Rhodes introduced the idea of the fundamental group of a group acting on a topological space. His article contains summarized proofs of results and has been studied since then primarily because the category of transformation groups is more general than the category of topological spaces. In this article, a thorough study of Rhodes’s work is presented, providing examples to enrich the theory. Dr. James Montaldi from the University of Manchester has recently provided a more general and applicable approach Rhodes’s main theorem. His results are also analyzed here.
References
Rhodes, F. 1966. "On the Fundamental Group of a Transformation". Proceedings of the London Mathematical, s3-16 (1): 635-650 doi: 10.1112/plms/s3-16.1.635.
Dummit, D.; Foote, R.. "Abstract Algebra". John Wiley & Sons Canada, Limited, 2004. ISBN 9780471452348.
Munkres, J., 2000. "Topology". Prentice Hall, Incorporated, ISBN 9780131816299. URL http://books.google.com.ec/books?id=XjoZAQAAIAAJ.
Massey, W., 1991. "A Basic Course in Algebraic Topology". Graduate Texts in Mathematics. Springer-Verlag GmbH. ISBN 9780387974309.
Steckles, K.; Montaldi, J., 2013. "Classification of symmetry groups for planar n-body choreographies".
Kirillov, A., 2004. "Lectures on the Orbit Method". Graduate studies in mathematics. American Mathematical Society, ISBN 9780821835302.
Mitchell, S., 2012. "Topology of the orthogonal and unitary groups". Technical report, University of Washington, http://www.math.washington.edu/mitchell/Man/ou.pdf.
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