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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·7 papers on “4-manifolds” in Geometric Topology · 1 month

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 ↗

Exotic diffeomorphisms of reducible

4

-manifolds with odd

b_+

math.GT

This paper constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.

problem Detecting exotic diffeomorphisms on reducible 4-manifolds with odd b+.

method Using a families Bauer-Furuta invariant and pin-cobordism.

result Constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.

exotic diffeomorphisms 4-manifolds reducible odd b+Bauer-Furuta invariant

2026-06-30abs ↗pdf ↗

Deeply Slice Knot Detection via Immersed Curvesmath.GT

The paper tackles deeply slice knots via immersed curves.

problem Whether there exists a homology 3-sphere with certain knot properties.

method Constructing knots in contractible 4-manifolds and using Heegaard Floer homology invariants.

result Proves the existence of a class of deeply slice knots.

knot theory slice knots Heegaard Floer homology immersed curves 4-manifolds

2026-06-29abs ↗pdf ↗

Handle decompositions and the 1-dimensional inputs skein lasagna modulemath.GT

The paper calculates a new invariant for 4-manifolds using handle decompositions and skein relations.

problem Computing invariants for 4-manifolds built from handles.

method Handle attachment formulas, cabled colimits, lasso relation.

result Explicit calculations and partial vanishing results for specific 4-manifolds.

handle decompositions skein relations 4-manifolds Khovanov module Rozansky-Willis homologies

2026-06-28abs ↗pdf ↗

Homotopy Coherent Nielsen Realization Problem for Dehn Twists on K3-Type 4-Manifoldsmath.GT

Dehn twists on K3-type 4-manifolds are not homotopy coherently Nielsen realizable.

problem Homotopy coherent Nielsen realization problem for Dehn twists on 4-manifolds

method Using family Seiberg-Witten theory

result Failure of the classical Nielsen realization problem in K3-type 4-manifolds

Dehn twists K3-type 4-manifolds Nielsen realization Seiberg-Witten theory

2026-06-23abs ↗pdf ↗

Links of Mazur manifolds and exoticamath.GT

Construct non-split 2-component links in $S^4$ to produce exotic pairs of 4-manifolds

problem Construct non-split 2-component links in

S^4

method Construct non-split 2-component links in

S^4

result Obtain exotic pairs of simply connected, definite 4-manifolds with boundary

Mazur manifolds exotic pairs 4-manifolds exotic embeddings

2026-06-23abs ↗pdf ↗