Frobenius Pairs and Atiyah Duality
نویسنده
چکیده
We define a notion of “Frobenius pair”, which is a mild generalization of the notion of “Frobenius object” in a monoidal category. We then show that Atiyah duality for smooth manifolds can be encapsulated in the statement that a certain collection of structure obtained from a manifold forms a “commutative Frobenius pair” in the stable homotopy category of spectra.
منابع مشابه
Singularities with Symmetries, Orbifold Frobenius Algebras and Mirror Symmetry
Previously, we introduced a duality transformation for Euler G– Frobenius algebras. Using this transformation, we prove that the simple A,D,E singularities and Pham singularities of coprime powers are mirror self– dual where the mirror duality is implemented by orbifolding with respect to the symmetry group generated by the grading operator and dualizing. We furthermore calculate orbifolds and ...
متن کاملMicrobundles and Thom Classes
In this note we introduce Thorn classes of microbundles. We determine the Thorn class of the Whitney sum as the cup product of Thorn classes and state two applications ; one to Gysin sequences of Whitney sums and one to the Atiyah-Bott-Shapiro duality theorem for Thorn spaces (cf. Atiyah [2]). Thus our main result states tha t for microbundles /xi, JU2 over a compact (topological) manifold X, i...
متن کاملExtention Cohomological Fields Theory and Noncommutative Frobenius Manifolds
INTRODUCTION The Cohomological Field Theory was propose by Kontsevich and Manin [5] for description of Gromov-Witten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F , satisfying to associative equations. In points of convergence the series F defines a Frobenius algebras. The set of these po...
متن کاملOn Almost Duality for Frobenius Manifolds
We present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg Witten duality.
متن کاملDuality, Central Characters, and Real-valued Characters of Finite Groups of Lie Type
We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...
متن کامل