Configuration Spaces of Manifolds with Boundary

Campos, Ricardo; Idrissi, Najib; Lambrechts, Pascal; Willwacher, Thomas

doi:10.48550/arxiv.1802.00716

Cited by 8 publications

(11 citation statements)

References 25 publications

(76 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Idrissi's result provides a generalization of Knudsen's description of the factorization homology for higher enveloping algebras of Lie algebras [39]. The paper [13] provides an extension of the constructions of [14,38] for manifolds with boundary, while the paper [12] addresses an extension of the definition of these operadic module structures by using a framed version of the operads of little discs.…”

Section: Discussionmentioning

confidence: 99%

Little discs operads, graph complexes and Grothendieck-Teichmüller groups

Fresse¹

2020

Handbook of Homotopy Theory

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Little discs operads, graph complexes and Grothendieck-Teichmüller groups

Fresse¹

2020

Handbook of Homotopy Theory

View full text Add to dashboard Cite

show abstract

“…, 2k}. † † The stratification of the conpactification of configuration spaces of manifolds with boundary is described in [CILW,§3.6].…”

Section: Evaluation Of the Configuration Space Integralsmentioning

confidence: 99%

Addendum to: Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$ (homological interpretation)

Watanabe¹

2021

Preprint

View full text Add to dashboard Cite

In this addendum, we give a differential form interpretation of the proof of the main theorem of [Wa3], which gives lower bounds of the dimensions of π k (BDiff(D 4 , ∂)) ⊗ Q in terms of the dimensions of Kontsevich's graph homology, and explain why it can be extended to arbitrary even dimensions d ≥ 4. We attempted to make the proof accessible to more readers. Thus we do not assume familiarity with configuration space integrals nor knowledge of finite type invariants. Part of this addendum might be joined to the original article when it will be re-submitted to the journal. This is not aimed at giving a correction to the previous version.). This has the structure of a manifold with corners induced from C r (R d ). § This sequence of blow-ups is different from the analogue of the successive blow-ups given in [FM, AS] in their derivation of the definition from (2.4). The sequence of blow-ups along (2.5) will be convenient for our purpose.¶ In [Si], Cn(X), C * r (V ), S A are denoted like Cn[X], Cr(V ), C T (X), respectively.

show abstract

“…. 18 Usually, the BV space of fields is given by the (−1)-shifted cotangent bundle of the BRST space of fields, i.e. FBV = T * [−1]FBRST.…”

Section: The Bv-bfv Formalismmentioning

confidence: 99%

4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism

Moshayedi¹

2021

Preprint

View full text Add to dashboard Cite

We study the behavior of Donaldson's invariants of 4-manifolds based on the moduli space of anti self-dual connections (instantons) in the perturbative field theory setting where the underlying source manifold has boundary. It is well-known that these invariants take values in the instanton Floer homology groups of the boundary 3-manifold. Gluing formulae for these constructions lead to a functorial topological field theory description according to a system of axioms developed by Atiyah, which can be also regarded in the setting of perturbative quantum field theory, as it was shown by Witten, using a version of supersymmetric Yang-Mills theory, known today as Donaldson-Witten theory. One can actually formulate an AKSZ model which recovers this theory for a certain gauge-fixing. We consider these constructions in a perturbative quantum gauge formalism for manifolds with boundary that is compatible with cutting and gluing, called the BV-BFV formalism, which was recently developed by Cattaneo, Mnev and Reshetikhin. We prove that this theory satisfies a modified Quantum Master Equation and extend the result to a global picture when perturbing around constant background fields. These methods are expected to extend to higher codimensions and thus might help getting a better understanding for fully extendable n-dimensional field theories (in the sense of Baez-Dolan and Lurie) in the perturbative setting, especially when n ≤ 4. Additionally, we relate these constructions to Nekrasov's partition function by treating an equivariant version of Donaldson-Witten theory in the BV formalism. Moreover, we discuss the extension, as well as the relation, to higher gauge theory and enumerative geometry methods, such as Gromov-Witten and Donaldson-Thomas theory and recall their correspondence conjecture for general Calabi-Yau 3-folds. In particular, we discuss the corresponding (relative) partition functions, defined as the generating function for the given invariants, and gluing phenomena. 3.2. The (holomorphic) Chern-Simons action functional 3.3. A 4D-3D bulk-boundary correspondence on (infinite) cylinders 3.4. Instanton Floer homology 3.5. Relation to Donaldson polynomials 3.6. Field theory approach to instanton Floer homology 3.7. Lagrangian Floer homology 3.8. The Atiyah-Floer conjecture 4. The BV-BFV formalism 4.1. BV formalism 4.1.1. Quantization 4.2. BV algebras 4.3. BFV formalism 4.4. BV-BFV formalism 4.4.1. Quantization 4.5. Gluing of BV-BFV partition functions 4.6. Example: abelian BF theory 4.7. BV-BF k V extension and shifted symplectic structures 5. AKSZ formulation of DW theory 5.1.

show abstract

Configuration Spaces of Manifolds with Boundary

Cited by 8 publications

References 25 publications

Little discs operads, graph complexes and Grothendieck-Teichmüller groups

Little discs operads, graph complexes and Grothendieck-Teichmüller groups

Addendum to: Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$ (homological interpretation)

4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism

Contact Info

Product

Resources

About