Non-null framed bordant simple Lie groups
Haruo Minami

TL;DR
This paper revisits the classification of compact simple Lie groups with left invariant framings that are non-null framed bordant, offering a new verification approach to existing results using a refined product formula.
Contribution
It introduces a more ingenious verification formula for non-null framed bordantness, enhancing the understanding of the bordism classes of simple Lie groups.
Findings
Verification formula for non-null framed bordantness
Application to known classification results
Refined use of the decomposition formula
Abstract
Let be a compact simple Lie group equipped with the left invariant framing . It is known that there are several groups such that is non-null framed bordant. Previously we gave an alternative proof of these results using the decomposition formula of its bordism class into a Kronecker product by E. Ossa. In this note we propose a verification formula by reconsidering it, through a little more ingenious in the use of this product formula, and try to apply it to the non-null bordantness results above.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Geometric Analysis and Curvature Flows
