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The L²-invariants and Morse numbers

Vladimir V. Sharko (2009)

Banach Center Publications

We study the homotopy invariants of free cochain complexes and Hilbert complexes. These invariants are applied to calculation of exact values of Morse numbers of smooth manifolds.

The Łojasiewicz gradient inequality in a neighbourhood of the fibre

Janusz Gwoździewicz, Stanisław Spodzieja (2005)

Annales Polonici Mathematici

Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.

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