Smooth constructions of homotopy-coherent actions
SCIE
SCOPUS
- Title
- Smooth constructions of homotopy-coherent actions
- Authors
- OH, YONG GEUN; Tanaka, Hiro Lee
- Date Issued
- 2022-08
- Publisher
- Geometry & Topology Publications
- Abstract
- We prove that, for nice classes of infinite-dimensional smooth groups
G
, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of
G
. 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
B
G
are naturally equivalent to the (continuous) homotopy groups, and a second showing that a particular strict category localizes to yield the homotopy type of
B
G
.
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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/113653
- DOI
- 10.2140/agt.2022.22.1177
- ISSN
- 1472-2747
- Article Type
- Article
- Citation
- Algebraic and Geometric Topology, vol. 22, no. 3, page. 1177 - 1216, 2022-08
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