Algebraic cohomotopy groups, algebraic fundamental groups and stably free modules

2025/12/18 by Sridharan, Raja, Upadhyay, Sumit Kumar
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2512.16664

Abstract

In this article, we prove the algebraic counterpart of the topological results H¹(S¹, ℤ) ≅ ℤ and H¹(S², ℤ) ≅ \0\. We also see that a non-trivial element of the algebraic cohomotopy groups of certain rings associated with some known topological spaces provides examples of non-free stably free module of rank two over those rings.

Citations

• Connection between commutative algebra and topology

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