Cornered Heegaard Floer Homology (Memoirs of the American Mathematical Society)

Douglas, Christopher L./ Lipshitz, Robert/ Manolescu, Ciprian

American Mathematical Society（2020/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 113 p.
• 言語 ENG
• 商品コード 9781470437718

Full Description

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.

Contents

Introduction
Some abstract 2-algebra
More 2-algebra: bending and smoothing
Some homological algebra of 2-modules
The algebras and algebra-modules
The cornering module-2-modules
The trimodules $\mathsf{T}_{DDD}$ and $\mathsf{T}_{DDA}$
Cornered 2-modules for cornered Heegaard diagrams
Gradings
Practical computations
The nilCoxeter planar algebra
Bibliography.