Rational and polynomial density on compact real manifolds

The rational homology of real toric manifolds

Toric manifolds. In a seminal paper [7] that appeared some twenty years ago, Michael Davis and Tadeusz Januszkiewicz introduced a topological version of smooth toric varieties, and showed that many properties previously discovered by means of algebro-geometric techniques are, in fact, topological in nature. Let P be an n-dimensional simple polytope with facets F1, . . . , Fm, and let χ be an in...

Surgery on Compact Manifolds

Characterizing Polynomial Time Computability of Rational and Real Functions

Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the computational complexity of real functions defined over compact domains has been extensively studied. However, much less have been done for other kinds of real function...

Polynomial Interpretations over the Natural, Rational and Real Numbers Revisited

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect to termination proving power, Lucas managed to prove in 2006 that there are rewrite systems that can be shown polynomially terminating by polynomial interpre...

Lipschitz Spaces on Compact Manifolds

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...