Formal Barycenter Spaces with Weights: The Euler Characteristic

Sadok Kallel

Formal Barycenter Spaces with Weights: The Euler Characteristic

Algebraic Topology 2019-02-07 v2 Analysis of PDEs

Authors: Sadok Kallel

Abstract

We compute the Euler characteristic with compact supports $\chi_c$ of the formal barycenter spaces with weights of a finite CW complex, connected or not. This reduces to the topological Euler characteristic $\chi$ when the weights of the singular points are less than one. As foresighted by A. Malchiodi, our formula is related to the Leray-Schauder degree for mean field equations on a compact Riemann surface obtained by C.C. Chen and C.S. Lin.

Keywords

euler characteristic kähler metrics general topology

Cite

@article{arxiv.1808.00038,
  title  = {Formal Barycenter Spaces with Weights: The Euler Characteristic},
  author = {Sadok Kallel},
  journal= {arXiv preprint arXiv:1808.00038},
  year   = {2019}
}

Comments

16 pages. Major revision including a proof simplification. Extension of the main result to non-necessarily compact spaces. The Euler characteristic computation extends now to barycenter spaces of interiors of even dimensional manifolds (possibly disconnected)

Formal Barycenter Spaces with Weights: The Euler Characteristic

Abstract

Keywords

Cite

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