Cornered Heegaard Floer Homology.
Douglas, Christopher L.
Cornered Heegaard Floer Homology. - 1st ed. - 1 online resource (124 pages) - Memoirs of the American Mathematical Society Series ; v.262 . - Memoirs of the American Mathematical Society Series .
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Some abstract 2-algebra -- 2.1. Rectangular 2-algebras -- 2.2. Rectangular algebra-modules and 2-modules -- 2.3. Motility hypotheses and tensor products -- 2.4. Sequential objects and restricted tensor products -- 2.5. Module-2-modules, algebra-bimodules, and bimodule-modules -- Chapter 3. More 2-algebra: Bending and smoothing -- 3.1. The top-right bent tensor product -- 3.2. 2-modules as bent modules -- 3.3. The smoothed tensor product -- 3.4. The bottom-left bent tensor product -- 3.5. \Ainf-2-modules -- Chapter 4. Some homological algebra of 2-modules -- Chapter 5. The algebras and algebra-modules -- 5.1. The algebra associated to a matched circle -- 5.2. The algebra-modules associated to matched intervals -- 5.3. Gluing surfaces with boundary -- Chapter 6. The cornering module-2-modules -- 6.1. The \DD identity module-bimodule -- 6.2. The \DhAA- and \AhDD-cornering modules -- 6.3. The other cornering modules -- Chapter 7. The trimodules \trimod_ and \trimod_ -- 7.1. Combinatorial descriptions of the trimodules -- 7.2. Computation of \TDDD -- 7.3. Computation of \TDDA -- Chapter 8. Cornered 2-modules for cornered Heegaard diagrams -- 8.1. Cornered Heegaard diagrams -- 8.2. Definition of the cornered 2-modules -- 8.3. Tensor products of cornering module-2-modules -- 8.4. Proofs of the invariance and gluing theorems -- Chapter 9. Gradings -- 9.1. Noncommutative gradings -- 9.2. Gradings on the cornered 2-algebras, algebra-modules, and 2-modules -- 9.3. The graded pairing theorem -- Chapter 10. Practical computations -- 10.1. Induction and restriction functors -- 10.2. The multiplicity-one 2-algebra -- 10.3. An example -- Chapter 11. The nilCoxeter planar algebra -- Bibliography -- Back Cover.
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.
9781470455057
Floer homology.
Electronic books.
QA665 / .D684 2019
516.36
Cornered Heegaard Floer Homology. - 1st ed. - 1 online resource (124 pages) - Memoirs of the American Mathematical Society Series ; v.262 . - Memoirs of the American Mathematical Society Series .
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Some abstract 2-algebra -- 2.1. Rectangular 2-algebras -- 2.2. Rectangular algebra-modules and 2-modules -- 2.3. Motility hypotheses and tensor products -- 2.4. Sequential objects and restricted tensor products -- 2.5. Module-2-modules, algebra-bimodules, and bimodule-modules -- Chapter 3. More 2-algebra: Bending and smoothing -- 3.1. The top-right bent tensor product -- 3.2. 2-modules as bent modules -- 3.3. The smoothed tensor product -- 3.4. The bottom-left bent tensor product -- 3.5. \Ainf-2-modules -- Chapter 4. Some homological algebra of 2-modules -- Chapter 5. The algebras and algebra-modules -- 5.1. The algebra associated to a matched circle -- 5.2. The algebra-modules associated to matched intervals -- 5.3. Gluing surfaces with boundary -- Chapter 6. The cornering module-2-modules -- 6.1. The \DD identity module-bimodule -- 6.2. The \DhAA- and \AhDD-cornering modules -- 6.3. The other cornering modules -- Chapter 7. The trimodules \trimod_ and \trimod_ -- 7.1. Combinatorial descriptions of the trimodules -- 7.2. Computation of \TDDD -- 7.3. Computation of \TDDA -- Chapter 8. Cornered 2-modules for cornered Heegaard diagrams -- 8.1. Cornered Heegaard diagrams -- 8.2. Definition of the cornered 2-modules -- 8.3. Tensor products of cornering module-2-modules -- 8.4. Proofs of the invariance and gluing theorems -- Chapter 9. Gradings -- 9.1. Noncommutative gradings -- 9.2. Gradings on the cornered 2-algebras, algebra-modules, and 2-modules -- 9.3. The graded pairing theorem -- Chapter 10. Practical computations -- 10.1. Induction and restriction functors -- 10.2. The multiplicity-one 2-algebra -- 10.3. An example -- Chapter 11. The nilCoxeter planar algebra -- Bibliography -- Back Cover.
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.
9781470455057
Floer homology.
Electronic books.
QA665 / .D684 2019
516.36