Handle decomposition complexity and representation spaces
Paolo Aceto, Aliakbar Daemi, Jennifer Hom, Tye Lidman, JungHwan Park

TL;DR
This paper investigates the handle decomposition complexity of certain homology three-spheres that bound definite four-manifolds, utilizing the homology cobordism invariant from instanton Floer homology to establish new constraints.
Contribution
It proves that some homology three-spheres bounding definite four-manifolds require complex handle decompositions, revealing new topological obstructions.
Findings
Certain homology three-spheres must have complex handle decompositions
The invariant provides obstructions to simple bounding four-manifolds
Handle complexity relates to the homology cobordism invariant
Abstract
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homology cobordism invariant from instanton Floer homology.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras
