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The AKSZ construction in derived algebraic geometry as an extended topological field theory / Damien Calaque, Rune Haugseng, Claudia Scheimbauer

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 308, number 1555 (April 2025)Publisher: Providence, RI : American Mathematical Society, April 2025Description: v, 173 SeitenISBN:
  • 9781470472726
Additional physical formats: 9781470481421 | Erscheint auch als: The AKSZ construction in derived algebraic geometry as an extended topological field theory. Online-Ausgabe Providence, RI : American Mathematical Society, 2025. 1 Online-Ressource (v, 173 Seiten)MSC: MSC: 14-02 | 14A30 | 18N65 | 57R56 | 14D21 | 14J42 | 53D30RVK: RVK: SI 130Summary: Summary: We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological version of the classical AKSZ field theories that occur in physics. These have as their targets higher categories of symplectic derived stacks, with higher morphisms given by iterated Lagrangian correspondences. We define these, as well as analogous higher categories of oriented derived stacks and iterated oriented cospans, and prove that all objects are fully dualizable. Then we set up a functorial version of the AKSZ construction, first implemented in this context by Pantev-Toën-Vaquié-Vezzosi, and show that it induces a family of symmetric monoidal functors from oriented stacks to symplectic stacks. Finally, we construct forgetful functors from the unoriented bordism (∞,n)-category to cospans of spaces, and from the oriented bordism (∞,n)-category to cospans of spaces equipped with an orientation; the latter combines with the AKSZ functors by viewing spaces as constant stacks, giving the desired field theories.Summary: Keywords: Derived Stacks, Shifled Symplectic Structures, Lagrangian Correspondences, Topological Field Theories, AKSZ Construction, (∞,n)-categoriesPPN: PPN: 1926031679
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Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-308.2025,1555 Nicht ausleihbar
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