Related papers: Equivariant Morse theory and quantum integrability
We show that, in addition to the quantizations of the rational numbers discovered by Morier-Genoud and Ovsienko, there exist a pair of conjugate representations of the modular group and the corresponding equivariant maps with respect to…
Following ideas of Lurie, we give in this article a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain in particular equivariant spectra…
We introduce the most general to date version of the permutation-equivariant quantum K-theory, and express its total descendant potential in terms of cohomological Gromov-Witten invariants. This is the higher-genus analogue of adelic…
Using projective spaces as examples of toric manifolds, we examine K-theoretic fixed point localization. On the one hand, we will see how the permutation-equivariant theory of the point target space emerges as a necessary ingredient. On the…
We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups - in the sense of Kustermans and Vaes - following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Ehrhart theory is the study of the enumeration of lattice points in lattice polytopes. Equivariant Ehrhart theory is a generalization of Ehrhart theory that takes into account the action of a finite group acting via affine transformations…
We develop the approach via quasihomomorphisms and the universal algebra $qA$ to Kasparov's $KK$-theory, so as to cover versions of $KK$ such as $KK^{nuc}$, $KK^G$ and ideal related $KK$-theory.
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any…
On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…
This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
We provide the geometric construction of a series of generalized Schur algebras of any type via Borel-Moore homologies and equivariant K-groups of generalized Steinberg varieties. As applications, we obtain a Schur algebra analogue of the…
We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…
We construct a topos of quantum sets and embed into it the classical topos of sets. We show that the internal logic of the topos of sets, when interpreted in the topos of quantum sets, provides the Birkhoff-von Neumann quantum propositional…
In this paper, we construct cochain complexes generated by the cohomology of critical manifolds in the abstract setup of flow categories for Morse-Bott theories under minimum transversality assumptions. We discuss the relations between…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous…