The directed distance between homotopy classes of critical Sobolev self-maps of spheres equals an explicit constant times the difference in their Brouwer degrees.
The topology of four-dimensional manifolds
10 Pith papers cite this work. Polarity classification is still indexing.
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Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
Derives Pohozaev compatibility between weak limit and bubble involving the Weyl tensor for Yang-Mills bubbling on general 4-manifolds, extending Yin's obstructions and ruling out some bubbling on CP2.
A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.
T-positive links are precisely the strongly quasipositive links that are closures of T-homogeneous braids, strictly containing non-split braid positive links, with all strongly quasipositive fibered knots up to 12 crossings being T-positive.
An explicit maw dual graph construction extracts the Thurston norm from sutured manifold hierarchies, yielding computations for three-component pretzel link exteriors and a theorem that certain nonseparating surfaces in Haken manifolds lie outside open top-dimensional cones of the norm ball.
Establishes exact correspondence between diffusion sampling and adiabatic ground-state transport in Score Hamiltonians, yielding density reconstruction bounds and a fundamental sampling limit given by squared score error over spectral gap.
Exotic differential structures on S^7 produce different Dirac operator spectra for specific symmetric gauge potentials in the Kaluza-Klein limit, implying different physical laws on topologically identical manifolds.
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
citing papers explorer
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The distance between homotopy classes of Sobolev maps on spheres
The directed distance between homotopy classes of critical Sobolev self-maps of spheres equals an explicit constant times the difference in their Brouwer degrees.
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Exotic aspherical 4-manifolds
Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
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Pohozaev identities and bubbling obstruction for Yang-Mills fields in conformal dimension
Derives Pohozaev compatibility between weak limit and bubble involving the Weyl tensor for Yang-Mills bubbling on general 4-manifolds, extending Yin's obstructions and ruling out some bubbling on CP2.
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Small Triangulations of $4$-Manifolds: Introducing the $4$-Manifold Census
A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.
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On T-positive links
T-positive links are precisely the strongly quasipositive links that are closures of T-homogeneous braids, strictly containing non-split braid positive links, with all strongly quasipositive fibered knots up to 12 crossings being T-positive.
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Sutured manifold hierarchies and the Thurston nom
An explicit maw dual graph construction extracts the Thurston norm from sutured manifold hierarchies, yielding computations for three-component pretzel link exteriors and a theorem that certain nonseparating surfaces in Haken manifolds lie outside open top-dimensional cones of the norm ball.
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The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
Establishes exact correspondence between diffusion sampling and adiabatic ground-state transport in Score Hamiltonians, yielding density reconstruction bounds and a fundamental sampling limit given by squared score error over spectral gap.
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Physics on manifolds with exotic differential structures
Exotic differential structures on S^7 produce different Dirac operator spectra for specific symmetric gauge potentials in the Kaluza-Klein limit, implying different physical laws on topologically identical manifolds.
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General Relativity via differential forms -- explorations in Plebanski's Formalism for GR
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.