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.
Researchers found nonsmoothable actions of Z2 * Z2 on spin 4-manifolds.
Study Z2 harmonic functions with singularities on flat space.
A new lower bound on the complexity of a 3-manifold is given using the Z2-Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of quadrilateral discs.
Local positive definite Z2^n-superfunctions can be extended.
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of nonorientable surfaces into which such graphs may be embedded. In a previous paper by the authors, the problem of calculating whether a given *-graph in which all vertices have degree 4 or 6 admi…
We present an explicit algorithm for tessellating the algebraic surfaces (real 4-manifolds) F(n) embedded in CP3 defined by the equation z0^n + z1^n + z2^n + z3^n = 0 in the standard homogeneous coordinates [z0, z1, z2, z3], where n is any positive integer. Note that F(4) in particular is a K3 surface. Our tessellation…
New knot invariant from equivariant Heegaard Floer cohomology.
We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell-Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorit…
New bounds on 3-manifold complexity, characterizing Thurston geometry.
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
The study classifies manifolds realized as orbit spaces of non-free Z2^k actions.
Characterizes a general range decreasing group homomorphism.
Improved sample efficiency in semantic segmentation with rotation equivariant CNNs.
To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their classification in low dimensions. I furthermore discuss CFT const…
This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete simplification of a knot diagram D is a sequence of moves that transform D into a diag…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.
The paper proves that certain thin links have only Z2 torsion in Khovanov homology.
Develops differential KO-character to determine real vector bundles in multiples of 8.
The data required for heterotic string theory with gauge group G, which for anomaly cancellation reasons must either be E8 x E8 or Spin(32)/Z2, consist of the following: a ten-dimensional space-time X and a principal G-bundle P. The fields in the theory consist of: a metric on X, a connection on P and a B-field which i…