Adiabatic Fredholm Theory
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917853842636800 |
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| author | Bottman, Nathaniel Wehrheim, Katrin |
| author_facet | Bottman, Nathaniel Wehrheim, Katrin |
| contents | We develop a robust functional analytic framework for adiabatic limits. This framework consist of a notion of adiabatic Fredholm family, several possible regularity properties, and an explicit construction that provides finite dimensional reductions that fit into all common regularization theories. We show that thhese finite dimensional reductions inherit global continuity and differentiability properties from the adiabatic Fredholm family. Moreover, we indicate how to construct adiabatic Fredholm families that describe the adiabatic limits for the nondegenerate Atiyah-Floer conjecture and strip-shrinking in quilted Floer theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adiabatic Fredholm Theory Bottman, Nathaniel Wehrheim, Katrin Symplectic Geometry Functional Analysis 47H09, 53D40, 57R58, 58B15 We develop a robust functional analytic framework for adiabatic limits. This framework consist of a notion of adiabatic Fredholm family, several possible regularity properties, and an explicit construction that provides finite dimensional reductions that fit into all common regularization theories. We show that thhese finite dimensional reductions inherit global continuity and differentiability properties from the adiabatic Fredholm family. Moreover, we indicate how to construct adiabatic Fredholm families that describe the adiabatic limits for the nondegenerate Atiyah-Floer conjecture and strip-shrinking in quilted Floer theory. |
| title | Adiabatic Fredholm Theory |
| topic | Symplectic Geometry Functional Analysis 47H09, 53D40, 57R58, 58B15 |
| url | https://arxiv.org/abs/2412.01779 |