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Algebraic Topology from a Homotopical Viewpoint

- M. Aguilar, S. Gitler, C. Prieto
- Mathematics
- 13 June 2002

Introduction.- Basic Concepts and Notation.- Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy Groups.- Homotopy Extension and Lifting Properties.- CW-Complexes Homology.- Homotopy… Expand

Moduli Spaces of Semistable Sheaves on Singular Genus 1 Curves

- D. H. Ruip'erez, Ana Cristina L'opez Mart'in, Dar'io S'anchez G'omez, C. Prieto
- Mathematics
- 12 June 2008

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… Expand

A decomposition formula for equivariant stable homotopy classes

- W. Marzantowicz, C. Prieto
- Mathematics
- 1 June 2009

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… Expand

Fourier-Mukai transforms for coherent systems on elliptic curves

- D. H. Ruip'erez, C. Prieto
- Mathematics
- 10 March 2006

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… Expand

Equivariant homotopical homology with coefficients in a Mackey functor

- M. Aguilar, C. Prieto
- Mathematics
- 1 August 2007

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… Expand

Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces

- A. L. Almorox, C. Prieto
- Mathematics
- 1 October 2006

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… Expand

Quantum Hall effect on Riemann surfaces

- C. Prieto
- Mathematics
- 1 June 2009

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… Expand

Fourier-Mukai Transform and Adiabatic Curvature of Spectral Bundles for Landau Hamiltonians on Riemann Surfaces

- C. Prieto
- Mathematics
- 11 March 2006

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).… Expand

The relative spectral sequence of leray-serre for fibration pairs

- C. Prieto
- Mathematics
- 1979

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