Floer Field Philosophy

Wehrheim, Katrin

doi:10.1007/978-3-319-34139-2_1

Cited by 7 publications

(6 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(For the subbicategories of Calabi-Yau varieties this relation is expected to be a generalisation of mirror symmetry.) The bicategory Symp is discussed in detail in the review article [Weh,Sect. 3.5…”

Section: Symplectic Geometrymentioning

confidence: 99%

Lecture notes on two-dimensional defect TQFT

Carqueville

2018

Banach Center Publ.

View full text Add to dashboard Cite

These notes offer an introduction to the functorial and algebraic description of 2-dimensional topological quantum field theories 'with defects', assuming only superficial familiarity with closed TQFTs in terms of commutative Frobenius algebras. The generalisation of this relation is a construction of pivotal 2-categories from defect TQFTs. We review this construction in detail, flanked by a range of examples. Furthermore we explain how open/closed TQFTs are equivalent to Calabi-Yau categories and the Cardy condition, and how to extract such data from pivotal 2-categories.

show abstract

Section: Symplectic Geometrymentioning

confidence: 99%

Lecture notes on two-dimensional defect TQFT

Carqueville

2018

Banach Center Publ.

View full text Add to dashboard Cite

show abstract

“…The following isomorphism has been proven in [WW12a] and then proven in a different setting by Lekili and Lipyanskiy using a more geometric construction, see also [Weh16,3.5.8]. This last construction has been extended by Manolescu and Woodward to the setting of the category Symp: Theorem 2.9.…”

Section: Definition 23 (Extended Moduli Spaces)mentioning

confidence: 92%

Symplectic instanton homology: naturality, and maps from cobordisms

Cazassus

2019

Quantum Topol.

View full text Add to dashboard Cite

We prove that Manolescu and Woodward's Symplectic Instanton homology, and its twisted versions, are natural; and define maps associated to four dimensional cobordisms within this theory.This allows one to define representations of the mapping class group, the fundamental group and the first cohomology group with Z2 coefficients of a 3-manifold. We also provide a geometric interpretation of the maps appearing in the long exact sequence for symplectic instanton homology, together with vanishing criterions.

show abstract

“…We now define partial two-categories, as two categories where the compositions are only partially defined. These can be seen as 2category analogs of Wehrheim's categories with Cerf decompositions [Weh16]. In the next section we associate a strict 2-category to such partial 2-categories.…”

Section: Partial 2-categoriesmentioning

confidence: 99%

A two-category of Hamiltonian manifolds, and a (1+1+1) field theory

Cazassus¹

2019

Preprint

View full text Add to dashboard Cite

We define an extended field theory in dimensions 1 `1 1, that takes the form of a "quasi 2-functor" with values in a strict 2-category z Ham, defined as the "completion of a partial 2-category" Ham, notions which we define. Our construction extends Wehrheim and Woodward's Floer Field theory, and is inspired by Manolescu and Woodward's construction of symplectic instanton homology. It can be seen, in dimensions 1 `1, as a real analog of a construction by Moore and Tachikawa.Our construction is motivated by instanton gauge theory in dimensions 3 and 4: we expect to promote zHam to a (sort of) 3-category via equivariant Lagrangian Floer homology, and extend our quasi 2-functor to dimension 4, via equivariant analogues of Donaldson polynomials.

show abstract

Floer Field Philosophy

Cited by 7 publications

References 69 publications

Lecture notes on two-dimensional defect TQFT

Lecture notes on two-dimensional defect TQFT

Symplectic instanton homology: naturality, and maps from cobordisms

A two-category of Hamiltonian manifolds, and a (1+1+1) field theory

Contact Info

Product

Resources

About