ON QUANDLE HOMOLOGY GROUPS OF ALEXANDER QUANDLES OF PRIME ORDER

被引：20

作者：

Nosaka, Takefumi ^{[1
]}

机构：

[1] Kyoto Univ, Math Sci Res Inst, Sakyo Ku, Kyoto 6068502, Japan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2013年 / 365卷 / 07期

关键词：

Rack; quandle; homology; cohomology; knot; COHOMOLOGY; SURFACES;

D O I：

10.1090/S0002-9947-2013-05754-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we determine the integral quandle homology groups of Alexander quandles of prime order. As a special case, this settles the delayed Fibonacci conjecture by M. Niebrzydowski and J. H. Przytycki from their 2009 paper. Further, we determine the cohomology group of the Alexander quandle and obtain relatively simple presentations of all higher degree cocycles which generate the cohomology group. Finally, we prove that the integral quandle homology of a finite connected Alexander quandle is annihilated by the order of the quandle.

引用

页码：3413 / 3436

页数：24

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