Homological Properties of Constant-Energy Surfaces

It is of practical interest to answer the following question how many full tori (ordinary and n dimensional X 2 ) participate in gluing the manifold Q f Here 

Recall that in the case the number m of full tori S x is associated with stable periodic solutions of a system on and is, therefore, of special interest. First we describe two special cases. 

Case 2 A manifold Q is obtained by gluing two or several cylinders. In this case, one can obtain a manifold Q in which ZTi(Q, Z) = Z (for an example see 1 above). 

Having performed this operation on all the cylinders, we obtain a manifold glued without the help of cylinders. If a manifold Q is glued of cylinders only, then the described reduction process is, of course, impracticable. 

Theorem 2.3.2. If a three-dimensional connected manifold Q is glued of q oriented saddles, m full tori, and an arbitrary number s of nonoriented saddles and 

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