GENERATORS OFS¹-BORDISM

Abstract

An equation showing the dependence of electronic mobility in the paraffins on the number of carbon atoms in the molecule is proposed, and the degree to which it is in agreement with experimental results is examined. Further simplified equations, giving the relationship between electronic mobility and its associated activation energy with the number of carbon atoms in the molecule, and its length, are derived. The form of these equations indicates that, over a limited range, the activation energy is directly proportional to the number of carbon-hydrogen bonds in the molecule.

On Rigid Hirzebruch Genera

“…From this it follows that the theorem holds also for H = D a,b , a, b ∈ R, where R = Q or R. Moreover, (3.2) implies a proof for the case H = G a,b . We also can propose a proof which is based on multiplicative generators of U S 1 * [16], where U S 1 * is the bordisms ring of complex manifolds with circle actions. The idea of this proof is very natural: we just verify the theorem for generators that are given in [16] explicitly.…”

“…It is clear that rigidity of h for generators implies rigidity for all manifolds. Note that [16] gives a proof of the Atiyah -Hirzebruch theorem for the T y −genus.…”

“…We can repeat these proofs (with "signs" from [4]) practically without changes for the case R = C. Therefore, the theorem holds for T x,y , x, y ∈ C, genera, i. We also can propose a proof which is based on multiplicative generators of U S 1 * [16], where U S 1 * is the bordisms ring of complex manifolds with circle actions. The idea of this proof is very natural: we just verify the theorem for generators that are given in [16] explicitly.…”

“…We also can propose a proof which is based on multiplicative generators of U S 1 * [16], where U S 1 * is the bordisms ring of complex manifolds with circle actions. The idea of this proof is very natural: we just verify the theorem for generators that are given in [16] explicitly. It is clear that rigidity of h for generators implies rigidity for all manifolds.…”

Circle actions with two fixed points

“…where H is the characteristic series of h (see [3,8]). If h is rigid, then from (1) it follows that h(X) = S h ({w ij }, u) for any u.…”