تقرير
Algebraic string topology from the neighborhood of infinity
| العنوان: | Algebraic string topology from the neighborhood of infinity |
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| المؤلفون: | Rivera, Manuel, Takeda, Alex, Wang, Zhengfang |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Mathematics - Quantum Algebra, 16E40, 55P50, 18G10, 16S38 |
| الوصف: | We construct and study an algebraic analogue of the loop coproduct in string topology, also known as the Goresky-Hingston coproduct. Our algebraic setup, which under this analogy takes the place of the complex of chains on the free loop space of a possibly non-simply connected manifold, is the Hochschild chain complex of a smooth $A_{\infty}$-category equipped with a pre-Calabi-Yau structure and a trivialization of a version of the Chern character of its diagonal bimodule. The algebraic analogue of the loop coproduct is part of a more general mapping cone construction, which we describe in terms of the categorical formal punctured neighborhood of infinity associated to the underlying smooth $A_\infty$-category. We use a graphical formalism for $A_\infty$-categories and bimodules to describe explicit models for the operations and homotopies involved. We also compute explicitly the algebraic coproduct in the context of the string topology of spheres. Comment: 51 pages + Appendix. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.09684 |
| رقم الأكسشن: | edsarx.2308.09684 |
| قاعدة البيانات: | arXiv |
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