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.
Research resolves sign conventions in Floer theory for Morse-Bott case.
Researchers extend Higgs bundle theory to parabolic bundles, counting components.
We show that a Bott-Morse foliation in dimension 3 admits a linear, singular, Poisson structure of rank 2 with Bott-Morse singularities. We provide the Poisson bivectors for each type of singular component, and compute the symplectic forms of the characteristic distribution.
We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott--Morse theory on the corresponding moduli spaces.
We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the configuration space. Its critical points are described and Bott-Morse indices are co…
We develop techniques for computing the integer valued SU(3) Casson invariant. Our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the perturbed flat moduli space. These techniques, together with Bott-Morse theory and the spl…
We study codimension one (transversally oriented) foliations $\fa$ on oriented closed manifolds having non-empty compact singular set $\sing(\fa)$ which is locally defined by Bott-Morse functions. We prove that if the transverse type of $\fa$ at each singular point is a center and $\fa$ has a compact leaf with fini…
We study codimension one foliations with singularities defined locally by Bott-Morse functions on closed oriented manifolds. We carry to this setting the classical concepts of holonomy of invariant sets and stability, and prove a stability theorem in the spirit of the local stability theorem of Reeb. This yields, among…
In this paper, we consider generalized moment maps for Hamiltonian actions on -twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact …
We compute the Bott-Morse Floer cohomology of the Clifford torus in $\CP^n$ with all possible spin-structures. Each spin structure is known to determine an orientation of the moduli space of holomorphic discs, and we analyze the change of orientation according to the change of spin structure of the Clifford torus. Also…
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
Survey of Floer theories and their connections.
Lectures on topological field theories and differential cohomology.
The paper defines strong emergence in field theories and proves it exists between certain theories.
Topological string theory derived from string geometry for non-perturbative effects.
New cohomology theory for Lie 2-algebras extends classical theory.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory.
Researchers find new -conifolds in -theory with potential field theory duals.
We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, a…
New theory captures framing anomaly in gauge theory.
Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.
Survey on algebraic K- and L-theory conjecture.
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes rema…
String theory connects lattice models, links, and geometric Langlands.
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one term and two term (rack) homology theori…
Recent work connects Thompson's groups to knot theory.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
This thesis proposes a global geometric formulation of Extended Field Theories.
The paper quantizes hybrid topological-holomorphic field theories on .
This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory. Some proofs have been improved and …
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice of such a structure, but not on a choice of metric and in this sense, it is topo…
Cohomotopy theory predicts M-theory anomaly cancellation on 8-manifolds.
The paper extends Alexander and Markov theories to generalized knot theories.
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.
Abstract: Linking field theory to Floer theory via regularization.
Unified treatment of gauge theories and Yang-Mills theory duality.
New theory connects string theory to swampland distance conjecture.
Identifies all perturbative vacua in bosonic string theory.
In this short note we show how Dubrovin's integrable hierarchies, defined using the Gromov-Witten theory of a closed symplectic manifold, generalizes to Hamiltonian Floer theory. In particular, we show how the required generalization of the PSS isomorphism, relating Gromov-Witten theory and Hamiltonian Floer theory, ca…
Anomaly in free fermion theory revealed in functorial field theory.
Lecture notes on gauge theory for manifold invariants.
Semisimple 4D field theories can't distinguish smooth 4-manifolds.
Paper introduces a new geometric homology theory and applies it to Gromov-Witten theory.
New geometric approach realizes 5D bulk theories with 4D edge modes.