ar X iv : 0 90 8 . 31 74 v 2 [ m at h . C O ] 1 2 Se p 20 09 MÖBIUS TRANSFORM , MOMENT - ANGLE COMPLEXES AND HALPERIN – CARLSSON CONJECTURE
نویسنده
چکیده
In this paper, we give an algebra–combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley–Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex ZK (resp. real moment-angle complex RZK) of K, we show that the Halperin–Carlsson conjecture holds for ZK (resp. RZK) under the restriction of the natural T -action on ZK (resp. (Z2) -action on RZK).
منابع مشابه
. C O ] 2 1 A ug 2 00 9 MÖBIUS TRANSFORM , MOMENT - ANGLE COMPLEXES AND HALPERIN - CARLSSON CONJECTURE
In this paper, we give an algebra-combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley-Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex...
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