|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Smooth constructions of
homotopy-coherent actions
Yong-Geun Oh and Hiro Lee Tanaka |
|
Algebraic & Geometric Topology 22 (2022) 1177–1216
|
Abstract |
|
We prove that, for nice classes of infinite-dimensional smooth groups , natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of . This yields a bridge between infinite-dimensional smooth groups and homotopy theory. The result relies on two computations: one showing that the diffeological homotopy groups of the Milnor classifying space are naturally equivalent to the (continuous) homotopy groups, and a second showing that a particular strict category localizes to yield the homotopy type of . We then prove a result in symplectic geometry: these methods are applicable to the group of Liouville automorphisms of a Liouville sector. The present work is written with an eye toward Oh and Tanaka (2019), where our constructions show that higher homotopy groups of symplectic automorphism groups map to Fukaya-categorical invariants, and where we prove a conjecture of Teleman from the 2014 ICM in the Liouville and monotone settings. |
PDF Access Denied
We have not been able to recognize your IP address
3.144.25.74
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
smooth approximation, Lie groups, group actions
|
Mathematical Subject Classification
Primary: 58B05, 58D05
|
References |
Publication
Received: 15 April 2020
Revised: 16 April 2021
Accepted: 1 June 2021
Published: 25 August 2022
|
Authors |
| Yong-Geun Oh | |
| Center for Geometry and
Physics Institute for Basic Science Pohang South Korea |
Department of Mathematics Pohang University of Science and Technology Pohang South Korea |
| Hiro Lee Tanaka | |
| Department of Mathematics Texas State University San Marcos, TX United States |
|
| http://www.hiroleetanaka.com | |
