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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/219764
Aspectes homotòpics de les àlgebres hipercommutatives
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Les àlgebres de Batalin-Vilkovisky són estructures rellevants en geometria, topologia i física matemàtica. Sota certes hipòtesis es pot construir una àlgebra hipercommutativa a partir d'una àlgebra de Batalin-Vilkovisky, que és una estructura relacionada amb la cohomologia quàntica i que generalitza les àlgebres commutatives. Aquestes condicions se satisfan en diversos contextos geomètrics. En aquest treball, s'introdueix i s'estudia una pregunta relacionada amb la invariància homotòpica en el pas de les àlgebres de Batalin-Vilkovisky a les hipercommutatives. S'explica la meva aventura a través de nombrosos intents de demostració fallits, i finalment s'exposa una solució parcial del problema.
The notion of Batalin Vilkovisky algebra plays an important role in geometry, topology and mathematical physics. Under some conditions, often present in geometric situations, one can obtain, from a Batalin-Vilkovisky algebra, a hypercommutative algebra structure, a structure related to quantum cohomology and generalizing the notion of commutative algebra. In this work, a question related to homotopy invariance in the passage from Batalin-Vilkovisky to hypercommutative algebras is introduced and addressed. My odyssey through several failed attemps to answer this question is explained and, at the end, a solution to a simplified version of the problem is proposed.
The notion of Batalin Vilkovisky algebra plays an important role in geometry, topology and mathematical physics. Under some conditions, often present in geometric situations, one can obtain, from a Batalin-Vilkovisky algebra, a hypercommutative algebra structure, a structure related to quantum cohomology and generalizing the notion of commutative algebra. In this work, a question related to homotopy invariance in the passage from Batalin-Vilkovisky to hypercommutative algebras is introduced and addressed. My odyssey through several failed attemps to answer this question is explained and, at the end, a solution to a simplified version of the problem is proposed.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Joana Cirici
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GARRIDO VILALLAVE, Roger. Aspectes homotòpics de les àlgebres hipercommutatives. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/219764