skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: MONOPOLES AND LANDAU-GINZBURG MODELS II: FLOER HOMOLOGY
This is the second paper of this series. We define the monopole Floer homol- ogy for 3-manifolds with torus boundary, extending the work of Kronheimer-Mrowka for closed 3-manifolds. The Euler characteristic of this Floer homology recovers the Milnor torsion invariant of the 3-manifold by a theorem of Meng-Taubes.  more » « less
Award ID(s):
1808794
PAR ID:
10168633
Author(s) / Creator(s):
Date Published:
Journal Name:
ArXivorg
ISSN:
2331-8422
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Gross, David; Yao, Andrew Chi-Chih; Yau, Shing-Tung (Ed.)
    Bordered Floer homology is an invariant for 3-manifolds with boundary, defined by the authors in 2008. It extends the Heegaard Floer homology of closed 3-manifolds, defined in earlier work of Zoltán Szabó and the second author. In addition to its conceptual interest, bordered Floer homology also provides powerful computational tools. This survey outlines the theory, focusing on recent developments and applications. 
    more » « less
  2. Gross, D; Yao, A C-C; Yau, S-T (Ed.)
    Bordered Floer homology is an invariant for 3-manifolds with boundary, defined by the authors in 2008. It extends the Heegaard Floer homology of closed 3-manifolds, defined in earlier work of Zoltán Szabó and the second author. In addition to its conceptual interest, bordered Floer homology also provides powerful computational tools. This survey outlines the theory, focusing on recent developments and applications. 
    more » « less
  3. We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show that this assignment is isotopy invariant. The proof relies on finding a simple generating set for the fundamental group of the “space of Heegaard diagrams,” and then showing that Heegaard Floer homology has no monodromy around these generators. In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds. 
    more » « less
  4. We show that there exist infinitely many closed 3–manifolds that do not embed in closed symplectic 4–manifolds, disproving a conjecture of Etnyre–Min–Mukherjee. To do this, we construct L–spaces that cannot bound positive- or negative-definite manifolds. The arguments use Heegaard Floer correction terms and instanton moduli spaces. 
    more » « less
  5. Given a double cover between 3-manifolds branched along a nullhomologous link, we establish an inequality between the dimensions of their Heegaard Floer homologies. We discuss the relationship with the L-space conjecture and give some other topological applications, as well as an analogous result for sutured Floer homology. 
    more » « less