On-device research index

arXiv research

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.

168,742 papers · 148 categories

Trend · papers per month

count % of corpus

7 results for “2-cobordisms”

Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logicmath.CT

Research categorizes 2-cobordisms and finds non-finitely axiomatizable equational theories.

problem Equational theories of local monoids in cobordism categories are not finitely axiomatizable.

method Introduced combinatorial data encoding

2

-cobordisms, constructed von-Neumann-regular extensions, and studied various quotients.

result Local monoids of

2\mathfrak{Cob}

do not have finitely axiomatizable equational theories.

cobordism equational logic von-Neumann-regular 2-cobordisms annular category

2020-02-03abs ↗pdf ↗

SO(3)

-invariant

G_2

-cobordismsmath.DG

Study $SO(3)$ -invariant $G_2$ -cobordisms on 6-manifolds.

problem Understanding stable 3-forms and

G_2

-structures on 6-manifolds.

method Investigate a bordism relation for closed

SL(3;\mathbb{C})

-structures via closed

G_2

-structures under

SO(3)

-symmetry and co-associative conditions.

result The bordism relation is irreflexive and induces a more rigid structure.

$G_2$-structures 6-manifolds bordism SO(3) symmetry co-associative

2020-01-05abs ↗pdf ↗

The diagrammatic Soergel category and sl(2) and sl(3) foamsmath.QA

We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other the category of (universal) sl(3) foams.

2009-09-18abs ↗pdf ↗

Fold maps, framed immersions and smooth structuresmath.GT

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting theorem for the spectrum representing the cohomology theory of fold maps. For even q…

2008-03-26abs ↗pdf ↗

An elliptic boundary value problem for

G_{2}

structuresmath.DG

We show that the $G_{2}$ holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular we establish the existence of certain $G_{2}$ cobordisms be…

2018-01-05abs ↗pdf ↗

Topological properties of closed

\widetilde{\mathrm{G}}_2

\mathrm{SL}(3;\mathbb{C})

and

\mathrm{SL}(3;\mathbb{R})^2

forms on manifoldsmath.AT

The paper classifies topological properties of specific geometric forms on manifolds.

problem Classifying topological properties of closed

\widetilde{\mathrm{G}}_2

\mathrm{SL}(3;\mathbb{C})

and

\mathrm{SL}(3;\mathbb{R})^2

forms.

method Algebraic and topological techniques, including characteristic classes and obstruction theory, with recent

h

-principles.

result Complete classification of closed

\mathrm{SL}(3;\mathbb{C})

forms up to homotopy.

G2 forms SL(3 C) forms SL(3 R)^2 forms

2023-09-28abs ↗pdf ↗

On the homotopy type of the space of Sullivan diagramsmath.AT

We study the homotopy type of the harmonic compactification of the moduli space of a 2-cobordism S with one outgoing boundary component, or equivalently of the space of Sullivan diagrams of type S on one circle. Our results are of two types: vanishing and non-vanishing. In our vanishing results we are able to show that…

2017-05-21abs ↗pdf ↗