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.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
We show that the group of smooth homotopy -spheres acts freely on the set of smooth manifold structures on a topological manifold which is homotopy equivalent to the real projective -space. We classify, up to diffeomorphism, all closed manifolds homeomorphic to the real projective -space. We also show that…
Classifies embeddings of certain 4-manifolds into 7-space.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
Classification of embeddings of certain 4-manifolds into 7-space.
The paper proves conditions for 4-manifolds to be parallelizable and non-existence results.
Let N be a closed, connected, smooth 4-manifold with H_1(N;Z)=0. Our main result is the following classification of the set E^7(N) of smooth embeddings N->R^7 up to smooth isotopy. Haefliger proved that the set E^7(S^4) with the connected sum operation is a group isomorphic to Z_{12}. This group acts on E^7(N) by embed…
We work in the smooth category. Let N be a closed connected n-manifold and assume that m>n+2. Denote by E^m(N) the set of embeddings N -> R^m up to isotopy. The group E^m(S^n) acts on E^m(N) by embedded connected sum of a manifold and a sphere. If E^m(S^n) is non-zero (which often happens for 2m<3n+4) then no results o…
New estimates show all stable Einstein manifolds are linear stable with respect to Perelman's ν-entropy.