• Corpus ID: 119045824

Calculating Euler-Poincare characteristic inductively

@article{Marjanovi2012CalculatingEC,
  title={Calculating Euler-Poincare characteristic inductively},
  author={Milosav M. Marjanovi{\'c}},
  journal={arXiv: Geometric Topology},
  year={2012}
}
  • M. Marjanović
  • Published 1 December 2012
  • Mathematics
  • arXiv: Geometric Topology
Motivated by decompositions of spaces that arise in continuous and discrete Morse theory, we describe a so called fibrous decomposition Z = X_0(Y_1)X_1 ... X_{n-1}(Y_n)X_n of a space Z. Among the applications is a succinct formula for the Euler-Poincare characteristic of Z, e(Z) = e(X_0) - e(Y_1) + e(X_1) - ... + e(X_{n-1}) - e(Y_n) + e(X_n) which exhibits the familiar sign pattern. A substantial part of the paper are examples demonstrating how the fibrous decomposition and consequently the… 

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