2011/04/10 by Yasuzo Ninshimura, Ninshimura, Yasuzo
Mathematics · #57M50 #57M60 #57S17 (Primary) 52B10 (Secondary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.CO #math.GT #msc:52B10 #msc:57M50 #msc:57M60 #msc:57S17
paper · pdf · doi:10.48550/arxiv.1104.1744
18 pages, 20 figures
arxiv created 2011/04/10 · arxiv updated 2015/03/18
A small cover was introduced by Davis and Januszkiewicz as an n-dimensional closed manifold with a locally standard Z2)n-action such that its orbit space is a simple convex polytope. There exist a one-to-one correspondence between small covers and (Z2)n-colored polytopes. In this paper we study a construction of 3-dimensional small covers by using two operations called a connected sum and a surgery. These operations correspondent to combinatorial operations on (Z2)3-colored simple convex polytopes. We shall show that each 3-dimensional small cover can be constructed from T3, RP3 and S1 × RP2 with two different (Z2)3-actions by using these operations. This result is a generalization and an improvement of Lü-Yu's result.