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Algebraic Topology from a Homotopical Viewpoint
Introduction.- Basic Concepts and Notation.- Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy Groups.- Homotopy Extension and Lifting Properties.- CW-Complexes Homology.- Homotopy
Moduli Spaces of Semistable Sheaves on Singular Genus 1 Curves
We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure-dimensional sheaves. Using them we establish new
A decomposition formula for equivariant stable homotopy classes
For any compact Lie group $G$, we give a decomposition of the group $\{X,Y\}_G^k$ of (unpointed) stable $G$-homotopy classes as a direct sum of subgroups of fixed orbit types. This is done by
Fourier-Mukai transforms for coherent systems on elliptic curves
We determine all the Fourier-Mukai transforms for coherent systems consisting of a vector bundle over an elliptic curve and a subspace of its global sections, showing that these transforms are
Equivariant homotopical homology with coefficients in a Mackey functor
Abstract Let M be a Mackey functor for a finite group G. In this paper, generalizing the Dold–Thom construction, we construct an ordinary equivariant homotopical homology theory H ∗ G ( − ; M ) with
Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces
Abstract Given a Hermitian line bundle L with a harmonic connection over a compact Riemann surface ( S , g ) of constant curvature, we study the spectral geometry of the corresponding twisted Dirac
Quantum Hall effect on Riemann surfaces
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic
Fourier-Mukai Transform and Adiabatic Curvature of Spectral Bundles for Landau Hamiltonians on Riemann Surfaces
We study the family of Landau Hamiltonians on a Riemann surface S by means of a Nahm transform and an integral functor related to the Fourier-Mukai transform associated to its jacobian variety J(S).