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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.

168,742 papers · 148 categories

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5 results for “non-homotopy”

On Finite domination and Poincaré dualitymath.AT

The paper shows plentiful non-homotopy finite Poincaré duality spaces.

problem The existence of non-homotopy finite Poincaré duality spaces.

method Constructing a finitely dominated Poincaré space with a non-trivial 2-divisible element in the reduced Grothendieck group.

result The existence of finitely dominated Poincaré spaces that are not homotopy finite.

Poincaré duality finite domination non-homotopy fundamental group Grothendieck group

2022-10-12abs ↗pdf ↗

Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometrymath.DG

The paper extends symplectic techniques to generalized complex geometry.

problem Creating stable generalized complex structures on high-dimensional manifolds.

method Introducing generalized Luttinger surgery and generalized Gluck twist.

result Produced stable generalized complex structures with non-homotopy-equivalent components.

generalized complex geometry symplectic structures Luttinger surgery Gluck twist path-connected components

2022-07-31abs ↗pdf ↗

Stably diffeomorphic manifolds and the realisation of modified surgery obstructionsmath.GT

The paper constructs infinitely many stably diffeomorphic but non-homotopy equivalent manifolds.

problem Realising modified surgery obstructions for stably diffeomorphic manifolds.

method Proving a realisation result for subsets of Kreck's modified surgery monoid.

result Infinitely many stably diffeomorphic but non-homotopy equivalent manifolds.

stably diffeomorphic manifolds homotopy equivalence modified surgery obstructions Kreck's monoid

2021-09-12abs ↗pdf ↗

Four-manifolds, two-complexes and the quadratic bias invariantmath.GT

New invariant detects non-homotopy equivalent 4-manifolds.

problem Detecting non-homotopy equivalent 4-manifolds.

method Extending Kreck and Schafer's doubling construction to 2-complexes with finite fundamental group.

result Existence of

k

closed smooth 4-manifolds that are stably diffeomorphic but not homotopy equivalent.

4-manifolds homotopy equivalence doubling construction finite fundamental group stably diffeomorphic

2024-12-19abs ↗pdf ↗

Covering instability for the existence of positive scalar curvature metricsmath.DG

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

problem Existence of positive scalar curvature metrics on non-orientable manifolds and their covers.

method Extends Schoen-Yau inductive descent approach to non-orientable manifolds.

result Examples of non-orientable manifolds with positive scalar curvature metrics on their orientation double covers but not on homotopy equivalent manifolds.

positive scalar curvature non-orientable manifolds orientation double cover Urysohn widths band width estimates

2025-06-16abs ↗pdf ↗