TL;DR
This paper introduces a specific Morse function on the special orthogonal group SO(n) and proves that it is perfect, providing insights into the topology of SO(n) through Morse theory.
Contribution
The work constructs and verifies a perfect Morse function on SO(n), advancing understanding of its topological structure.
Findings
Established a Morse function on SO(n)
Proved the function is perfect
Enhanced topological understanding of SO(n)
Abstract
In this work, we define a Morse function on SO(n) and show that this function is indeed a perfect Morse function.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology