Big Fundamental Groups: Generalizing Homotopy and Big Homotopy

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Title: Big Fundamental Groups: Generalizing Homotopy and Big Homotopy
Author: Penrod, Keith, Morehouse College
Publication Date: 2016-02-01
Decade: 2010-2019
Abstract: The concept of big homotopy theory was introduced by J. Cannon and G. Conner in [1]. In this paper, we seek to refine this theory by making a similar functor for specific cardinals instead of the class of all of them at the same time. It will be shown that for every topological space, there is a cardinal such that this new fundamental group agrees with the big fundamental group on that space. Between any two such functors, there is a natural transformation, including the big fundamental group and the fundamental group as classically defined in homotopy theory. KEYWORDS: Homotopy, big Homotopy, Mathematics
Document Type: text
Format: application/pdf
Medium: articles
Source: arXiv:1410.3088v1 [math.AT] org (February 2016)
Department: Department of Mathematics
Institution: Morehouse College
URL: https://arxiv.org/abs/1410.3088
Handle: http://hdl.handle.net/20.500.12322/mc.ir.fac.pub:2016_penrod_keith
Rights Statement: http://rightsstatements.org/vocab/InC/1.0/