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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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← all fields·2 papers on “4-manifolds” in Geometric Topology · 1 week

Knotted surfaces with simply-connected complementsmath.GT

Study knotted surfaces in simply-connected 4-manifolds with trivial boundary.

problem Locally flat, compact, genus g surfaces with boundary a fixed knot in simply-connected 4-manifolds with boundary the 3-sphere.

method Analyzes homology and isotopy of surfaces with trivial fundamental group complements.

result Homologous surfaces are topologically ambiently isotopic rel. boundary.

knot theory 4-manifolds fundamental group ambient isotopy homology

2026-07-16abs ↗pdf ↗

A novel construction of homotopy 4-spheres and real projective 4-spaces à la Cappell-Shanesonmath.GT

New homotopy 4-spheres and real projective 4-spaces created.

problem Creating new homotopy 4-spheres and real projective 4-spaces.

method Extending Cappell-Shaneson's construction to produce new sets of smooth 4-manifolds.

result Produces new collections of homotopy 4-spheres and real projective 4-spaces.

homotopy 4-spheres homotopy real projective 4-spaces Cappell-Shaneson construction 4-manifolds smooth 4-manifolds

2026-07-16abs ↗pdf ↗