Cohomological Rigidity and the Number of Homeomorphism Types for Small Covers over Prisms
نویسندگان
چکیده
In this paper we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimensional prism P(m) with m ≥ 3. We introduce two invariants from colored prisms and two invariants from ordinary cohomology ring, which form a complete invariant system of homeomophism types of all small covers over a prism in most cases. Then we show that the cohomological rigidity holds for all small covers over a prism (i.e., cohomology rings of all small cover over a P(m) determine their homeomorphism types). In addition, we also calculate the number of homeomorphism types of all small cover over a P(m).
منابع مشابه
Small Covers over Prisms
In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.
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