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OXTOP SIGNED

Low-dimensional topology in Oxford

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EC-Contrib. €

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 OXTOP project word cloud

Explore the words cloud of the OXTOP project. It provides you a very rough idea of what is the project "OXTOP" about.

corresponds    contain    invariants    alexander    band    algebras    techniques    simplify    seem    branches    floer    maps    yield    sequence    fox    few    pi    obstruction    cobordism    algebraic    slice    polynomial    thurston    arithmetic    bounds    hfk    counterexample    dimensional    hf    coefficients    admit    eacute    surface    tqft    concavity    gluing    classification    geometries    manifolds       surgery    spectral    bound    homology    experts    graph    111    absolute    structure    genus    unimodal    tqfts    understand    21    biological    structures    bordered    unknotting    description    geometric    happens    brings    mcg    conjecture    alternating    gnf    attacking    huh    relationship    group    surfaces    hence    aacute    decide    lm    khovanov    strategy    heegaard    log    smooth    geometrization    algebra    theoretic    knot    gauge    first    poincar    examples    correction    form    question    tori    links    ball    representations    spaces    ribbon    consists    tool   

Project "OXTOP" data sheet

The following table provides information about the project.

Coordinator
THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD 

Organization address
address: WELLINGTON SQUARE UNIVERSITY OFFICES
city: OXFORD
postcode: OX1 2JD
website: www.ox.ac.uk

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Project website http://people.maths.ox.ac.uk/juhasza/
 Total cost 1˙497˙422 €
 EC max contribution 1˙497˙422 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-05-01   to  2021-04-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD UK (OXFORD) coordinator 1˙497˙422.00

Map

 Project objective

This project aims to build a group that brings together experts in gauge-theoretic, geometric, and group-theoretic techniques. It consists of 4 branches.

1. Cobordism maps in knot Floer homology (HFK). Defined by the PI, these should yield invariants of surfaces in 4-manifolds. Hence, they could be used to bound the 4-ball genus and the unknotting number, providing a tool for finding a counterexample to the smooth 4-dimensional Poincaré conjecture, and to decide whether a given slice knot bounds a ribbon surface. The cobordism maps seem to yield a spectral sequence from Khovanov homology to HFK. An important biological application is an obstruction for two links to be related by a band surgery.

2. TQFTs. We use our classification of (21)-dimensional TQFTs in terms of GNF*-algebras and MCG representations to find new examples of such TQFTs. First, we simplify the algebraic structure, then determine when a GNF*-algebra corresponds to a (111)-dimensional TQFT. This would allow us to find a (21)-dimensional TQFT that is not (111)-dimensional.

3. Heegaard Floer (HF) homology and geometrization. There are currently few links known between Floer-theoretic invariants of 3-manifolds and the geometric structures they admit. We propose to study the Floer homology of arithmetic 3-manifolds. These are often L-spaces; the question is when this happens, and whether the HF correction terms contain any number-theoretic information. The next step is studying the relationship between HF and the Thurston geometries, and then gluing along tori via bordered Floer homology. An important step is to understand the behaviour of HF under covering maps.

4. The Fox conjecture. This states that the absolute values of the coefficients of the Alexander polynomial of an alternating knot form a unimodal sequence. We propose a strategy for attacking this conjecture via the graph-theoretic description of the Alexander polynomial due to Kálmán, and the test of log-concavity of Huh.

 Publications

year authors and title journal last update
List of publications.
2018 András Juhász, Marco Marengon
Computing cobordism maps in link Floer homology and the reduced Khovanov TQFT
published pages: 1315-1390, ISSN: 1022-1824, DOI: 10.1007/s00029-017-0368-9
Selecta Mathematica 24/2 2019-07-08
2018 András Juhász
Defining and classifying TQFTs via surgery
published pages: 229-321, ISSN: 1663-487X, DOI: 10.4171/qt/108
Quantum Topology 9/2 2019-07-08
2018 Andras Juhasz, Sungkyung Kang
Spectral order for contact manifolds with convex boundary
published pages: 3315-3338, ISSN: 1472-2747, DOI:
Algebraic and Geometric Topology 18/6 2019-04-14
2018 Daniele Celoria
On concordances in 3-manifolds
published pages: 180-200, ISSN: 1753-8416, DOI: 10.1112/topo.12051
Journal of Topology 11/1 2019-04-04
2018 Paolo Aceto, Marco Golla, Ana G. Lecuona
Handle decompositions of rational homology balls and Casson–Gordon invariants
published pages: 4059-4072, ISSN: 0002-9939, DOI: 10.1090/proc/14035
Proceedings of the American Mathematical Society 146/9 2019-04-09
2017 József Bodnár, Daniele Celoria, Marco Golla
A note on cobordisms of algebraic knots
published pages: 2543-2564, ISSN: 1472-2747, DOI: 10.2140/agt.2017.17.2543
Algebraic & Geometric Topology 17/4 2019-04-04

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