# Homology theories in low dimensional topology

Created: | 2017-02-03 13:41 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | The subject of homology theories in low-dimensional topology dates back to the work of Floer, and gained new breadth and vigour with the introduction of Khovanov homology fifteen years ago. Since then, these theories have had a far-reaching impact both in topology and more widely with analysts, algebraists, geometers, and physicists all contributing to and benefiting from their development. This programme will follow three broad themes:
The meaning of Floer homology: The programme will pursue and uncover intimate connections of Floer homology with underlying topological data. For example: the connection of Floer homology with the fundamental group by way of orderable groups, foliations, and related structures. The meaning of quantum knot homologies: In comparison to Floer homology, the geometrical meaning of quantum knot homologies such as Khovanov homology remains relatively obscure. One natural place to look for such meaning is in physics, which has played an important role in this field ever since Witten interpreted the Jones polynomial in terms of Chern-Simons theory. Quantum 3-manifold invariants: We hope to make significant progress towards, for example, lifting the numerical Reshetikhin-Turaev 3-manifold invariants to homological invariants. This should then provide a quantum counterpart to analytic invariants of smooth 4-manifolds. Tying these three themes together will be a central focus of the programme. It has become apparent in recent years that one should think of quantum invariants as first-order approximations to Floer invariants. The programme aims to make relationships such as these more precise and general. Figure from Ken Baker's Sketches of Topology blog |

# Media items

This collection contains 89 media items.

### Media items

#### 2-representations of braid groups, continued

Licata, A (Australian National University)

Friday 20th January 2017 - 14:30 to 15:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 7 Feb 2017

#### 2-Verma modules and the Khovanov-Rozansky link homologies

Vaz, P (Université Catholique de Louvain)

Thursday 29th June 2017 - 10:00 to 11:00

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 11 Jul 2017

#### 3-manifold groups epimorphisms and rigidity

Boileau, M (Université de Provence Aix Marseille 1)

Thursday 2nd February 2017 - 11:30 to 12:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 14 Feb 2017

#### A Gordon-Litherland form for ribbon surfaces

Owens, B (University of Glasgow)

Thursday 2nd February 2017 - 15:30 to 16:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 14 Feb 2017

#### An Upsilon-like invariant from Khovanov-Rozansky homology

Lewark, L

Tuesday 27th June 2017 - 13:30 to 14:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 20 Jul 2017

#### Annular Khovanov-Lee theory and representation theory

Grigsby, E (Boston College)

Thursday 19th January 2017 - 11:30 to 12:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 7 Feb 2017

#### Annular Khovanov-Lee theory of braid closures and braided surfaces

Grigsby, E (Boston College)

Thursday 19th January 2017 - 14:30 to 15:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 7 Feb 2017

#### Arborescent knots, mutants - current status on their invariants

Pichai, R (Indian Institute of Technology)

Tuesday 11th April 2017 - 14:30 to 15:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Apr 2017

#### Around Chebyshev's polynomial and the skein algebra of the torus

Queffelec, H

Monday 26th June 2017 - 16:00 to 17:00

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 19 Jul 2017

#### Bar Natan's deformation of Khovanov homology and involutive monopole Floer homology

Lin, F (Princeton University)

Thursday 20th April 2017 - 15:15 to 16:15

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 28 Apr 2017

#### Bordered via curves and train tracks I

Liam Watson

Friday 20th January 2017 - 09:00 to 10:00

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 7 Feb 2017

#### Boundary-reducing surgeries and bridge number

Luecke, J (University of Texas at Austin)

Wednesday 1st February 2017 - 11:30 to 12:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 14 Feb 2017

#### BPS states of M5-brane on T^3

Iqbal, A (Abdus Salam School of Mathematical Sciences GC University)

Thursday 13th April 2017 - 14:30 to 15:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Apr 2017

#### BPS states, knots and quivers

Sulkowski, P (Uniwersytet Warszawski, CALTECH (California Institute of Technology))

Thursday 13th April 2017 - 11:30 to 12:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Apr 2017

#### Braid groups and their 2-representations

Licata, A (Australian National University)

Tuesday 17th January 2017 - 14:30 to 15:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 6 Feb 2017

#### Braid monodromy, orderings, and transverse invariants

Plamenevskaya, O (Stony Brook University)

Thursday 16th March 2017 - 15:15 to 16:15

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 20 Mar 2017

#### Branched covers of quasipositive links and L-spaces

Boyer, S (UQAM - Université du Québec à Montréal)

Thursday 2nd February 2017 - 10:00 to 11:00

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 14 Feb 2017

#### Categorical diagonalization

Hogancamp, M

Wednesday 28th June 2017 - 11:30 to 12:30

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 20 Jul 2017

#### Categories of curved complexes for marked surfaces

Zibrowius, C (University of Cambridge)

Thursday 18th May 2017 - 15:15 to 16:15

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 24 May 2017

#### Categorified knot invariants and algebraic geometry

Negut, A (Massachusetts Institute of Technology)

Wednesday 28th June 2017 - 10:00 to 11:00

**Collection**:
Homology theories in low dimensional topology

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 11 Jul 2017