Polytopes, dualities, and Floer homology

Daniel Mathews

Polytopes, dualities, and Floer homology

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

Abstract

This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.

Original language	English
Title of host publication	CMA Proceedings
Subtitle of host publication	Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016
Editors	Peter Bouwknegt, Brett Parker, Bai-Ling Wang
Place of Publication	Canberra ACT Australia
Publisher	The Australian National University
Chapter	6
Pages	133-173
Number of pages	41
Volume	48
ISBN (Electronic)	9780648105626
Publication status	Published - 26 Apr 2019
Event	Gromov-Witten Theory, Gauge Theory and Dualities, 2016 - ANU Kioloa Coastal Campus, Kioloa, Australia Duration: 6 Jan 2016 → 16 Jan 2016 Conference number: 48th https://maths.anu.edu.au/research/cma-proceedings/gromov-witten-theory-gauge-theory-and-dualities-anukioloa-6-16-january-2016

Publication series

Name	Proceedings of the Centre for Mathematics and its Applications, Australian National University

Conference

Conference	Gromov-Witten Theory, Gauge Theory and Dualities, 2016
Country/Territory	Australia
City	Kioloa
Period	6/01/16 → 16/01/16
Other	The event consists of two parts, a series of introductory mini-courses held at the ANU Canberra from 6-9 Jan,2016 followed by an international conference at the ANU Kioloa campus, from 10-16 Jan, 2016. The aim of the mini-courses are to familiarise postgraduate students and early career researchers with some of the mathematical techniques for the study of moduli spaces from gauge theory and Gromov-Witten theory, while the conference brings together leading international researchers in this area.
Internet address	https://maths.anu.edu.au/research/cma-proceedings/gromov-witten-theory-gauge-theory-and-dualities-anukioloa-6-16-january-2016

Access to Document

287670023-oaFinal published version, 702 KB

https://maths.anu.edu.au/files/6polytopes_dualities_and_floer_homology.pdf

Quantum invariants and hyperbolic manifolds in three-dimensional topology
Purcell, J. & Mathews, D.
Australian Research Council (ARC), Monash University
1/01/16 → 31/07/20
Project: Research

Cite this

Mathews, D. (2019). Polytopes, dualities, and Floer homology. In P. Bouwknegt, B. Parker, & B.-L. Wang (Eds.), CMA Proceedings: Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016 (Vol. 48, pp. 133-173). (Proceedings of the Centre for Mathematics and its Applications, Australian National University). The Australian National University. https://maths.anu.edu.au/files/6polytopes_dualities_and_floer_homology.pdf

Mathews, Daniel. / Polytopes, dualities, and Floer homology. CMA Proceedings: Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016. editor / Peter Bouwknegt ; Brett Parker ; Bai-Ling Wang. Vol. 48 Canberra ACT Australia : The Australian National University, 2019. pp. 133-173 (Proceedings of the Centre for Mathematics and its Applications, Australian National University).

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abstract = "This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by K{\'a}lm{\'a}n, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with K{\'a}lm{\'a}n, we extend this story into contact topology and contact invariants in sutured Floer homology.",

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year = "2019",

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pages = "133--173",

editor = "Peter Bouwknegt and Brett Parker and Bai-Ling Wang",

booktitle = "CMA Proceedings",

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note = "Gromov-Witten Theory, Gauge Theory and Dualities, 2016 ; Conference date: 06-01-2016 Through 16-01-2016",

url = "https://maths.anu.edu.au/research/cma-proceedings/gromov-witten-theory-gauge-theory-and-dualities-anukioloa-6-16-january-2016",

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Mathews, D 2019, Polytopes, dualities, and Floer homology. in P Bouwknegt, B Parker & B-L Wang (eds), CMA Proceedings: Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016. vol. 48, Proceedings of the Centre for Mathematics and its Applications, Australian National University, The Australian National University, Canberra ACT Australia, pp. 133-173, Gromov-Witten Theory, Gauge Theory and Dualities, 2016, Kioloa, New South Wales, Australia, 6/01/16. <https://maths.anu.edu.au/files/6polytopes_dualities_and_floer_homology.pdf>

Polytopes, dualities, and Floer homology. / Mathews, Daniel.
CMA Proceedings: Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016. ed. / Peter Bouwknegt; Brett Parker; Bai-Ling Wang. Vol. 48 Canberra ACT Australia: The Australian National University, 2019. p. 133-173 (Proceedings of the Centre for Mathematics and its Applications, Australian National University).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

TY - GEN

T1 - Polytopes, dualities, and Floer homology

AU - Mathews, Daniel

N1 - Conference code: 48th

PY - 2019/4/26

Y1 - 2019/4/26

N2 - This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.

AB - This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.

M3 - Conference Paper

VL - 48

T3 - Proceedings of the Centre for Mathematics and its Applications, Australian National University

SP - 133

EP - 173

BT - CMA Proceedings

A2 - Bouwknegt, Peter

A2 - Parker, Brett

A2 - Wang, Bai-Ling

PB - The Australian National University

CY - Canberra ACT Australia

T2 - Gromov-Witten Theory, Gauge Theory and Dualities, 2016

Y2 - 6 January 2016 through 16 January 2016

ER -

Mathews D. Polytopes, dualities, and Floer homology. In Bouwknegt P, Parker B, Wang BL, editors, CMA Proceedings: Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, 6-16 January 2016. Vol. 48. Canberra ACT Australia: The Australian National University. 2019. p. 133-173. (Proceedings of the Centre for Mathematics and its Applications, Australian National University).

Polytopes, dualities, and Floer homology

Abstract

Publication series

Conference

Access to Document

Projects

Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this