Brunnian braids over the 2-sphere and Artin combed form
Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We...
Saved in:
Main Authors: | , |
---|---|
Other Authors: | |
Format: | Article |
Language: | English |
Published: |
2022
|
Subjects: | |
Online Access: | https://hdl.handle.net/10356/160042 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Nanyang Technological University |
Language: | English |
id |
sg-ntu-dr.10356-160042 |
---|---|
record_format |
dspace |
spelling |
sg-ntu-dr.10356-1600422022-07-12T02:07:15Z Brunnian braids over the 2-sphere and Artin combed form Duzhin, Fedor Loh, Jessica Sher En School of Physical and Mathematical Sciences School of Computer Science and Engineering Science::Mathematics Braid Groups Homotopy Groups of Spheres Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We give an interpretation of this exact sequence based on the combed form for braids over the sphere developed in [R. Gillette and J. V. Buskirk, The word problem and consequences for the braid groups and mapping class groups of the two-sphere, Trans. Amer. Math. Soc. 131 (1968) 277-296] with the aim of helping one to visualize the sequence and to do calculations based on it. 2022-07-12T02:07:15Z 2022-07-12T02:07:15Z 2021 Journal Article Duzhin, F. & Loh, J. S. E. (2021). Brunnian braids over the 2-sphere and Artin combed form. Journal of Knot Theory and Its Ramifications, 30(3), 2150012-1-2150012-9. https://dx.doi.org/10.1142/S0218216521500127 0218-2165 https://hdl.handle.net/10356/160042 10.1142/S0218216521500127 2-s2.0-85104355519 3 30 2150012-1 2150012-9 en Journal of Knot Theory and Its Ramifications © World Scientific Publishing Company. All rights reserved. |
institution |
Nanyang Technological University |
building |
NTU Library |
continent |
Asia |
country |
Singapore Singapore |
content_provider |
NTU Library |
collection |
DR-NTU |
language |
English |
topic |
Science::Mathematics Braid Groups Homotopy Groups of Spheres |
spellingShingle |
Science::Mathematics Braid Groups Homotopy Groups of Spheres Duzhin, Fedor Loh, Jessica Sher En Brunnian braids over the 2-sphere and Artin combed form |
description |
Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We give an interpretation of this exact sequence based on the combed form for braids over the sphere developed in [R. Gillette and J. V. Buskirk, The word problem and consequences for the braid groups and mapping class groups of the two-sphere, Trans. Amer. Math. Soc. 131 (1968) 277-296] with the aim of helping one to visualize the sequence and to do calculations based on it. |
author2 |
School of Physical and Mathematical Sciences |
author_facet |
School of Physical and Mathematical Sciences Duzhin, Fedor Loh, Jessica Sher En |
format |
Article |
author |
Duzhin, Fedor Loh, Jessica Sher En |
author_sort |
Duzhin, Fedor |
title |
Brunnian braids over the 2-sphere and Artin combed form |
title_short |
Brunnian braids over the 2-sphere and Artin combed form |
title_full |
Brunnian braids over the 2-sphere and Artin combed form |
title_fullStr |
Brunnian braids over the 2-sphere and Artin combed form |
title_full_unstemmed |
Brunnian braids over the 2-sphere and Artin combed form |
title_sort |
brunnian braids over the 2-sphere and artin combed form |
publishDate |
2022 |
url |
https://hdl.handle.net/10356/160042 |
_version_ |
1738844889122078720 |