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기하학 수리물리 연구단
기하학 수리물리 연구단
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Shrinking good coordinate systems associated to Kuranishi structures

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Title
Shrinking good coordinate systems associated to Kuranishi structures
Author(s)
Kenji Fukaya; Yong-Geun Oh; Hiroshi Ohta; Kaoru Ono
Publication Date
2016-12
Journal
JOURNAL OF SYMPLECTIC GEOMETRY, v.14, no.4, pp.1295 - 1310
Publisher
INT PRESS BOSTON
Abstract
The notion of good coordinate system was introduced by Fukaya and Ono in [FOn] in their construction of virtual fundamental chain via Kuranishi structure which was also introduced therein. This notion was further clarified in [FOOO1] in some detail. In those papers no explicit ambient space was used and hence the process of gluing local Kuranishi charts in the given good coordinate system was not discussed there. In our more recent writing [FOOO2, FOOO3], we use an ambient space obtained by gluing the Kuranishi charts. In this note we prove in detail that we can always shrink the given good coordinate system so that the resulting ‘ambient space’ becomes Hausdorff. This note is self-contained and uses only standard facts in general topology.
URI
https://pr.ibs.re.kr/handle/8788114/3211
ISSN
1527-5256
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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