Nilpotence in the symplectic bordism ring
Justin Noel
TL;DR
This paper establishes a complete set of conditions to determine when a stably symplectic manifold corresponds to a nilpotent element in the symplectic bordism ring, clarifying a longstanding folklore result.
Contribution
It provides a rigorous proof of a folklore result, characterizing nilpotent elements in the symplectic bordism ring through necessary and sufficient conditions.
Findings
Characterization of nilpotent elements in the symplectic bordism ring
Necessary and sufficient conditions for nilpotence
Clarification of a longstanding folklore result
Abstract
We prove a folklore result which gives a sequence of necessary and sufficient conditions for a stably symplectic manifold to define a nilpotent element in the symplectic bordism ring.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory