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
12 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.
The Spin-MInt algorithm is proven symplectic for general K electronic states via explicit verification of the condition MJM^T = J on the coadjoint orbit of the su(K) Lie-Poisson algebra.
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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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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.
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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.