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Kauffman bracket skein module of the connected sum of handlebodies and non-injectivity
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2021-05-05 , DOI: 10.1142/s0129167x21500427 Hiroaki Karuo 1
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2021-05-05 , DOI: 10.1142/s0129167x21500427 Hiroaki Karuo 1
Affiliation
For the handlebody H g of genus g , Przytycki studied the (Kauffman bracket) skein module 𝒮 q ( H n # H m ) of the connected sum H n # H m at q . One of his results is that, in the case when 1 − q k is invertible for any k ≠ 0 , a homomorphism φ : 𝒮 q ( H n ⊔ H m ) → 𝒮 q ( H n # H m ) is an isomorphism, which is induced by a natural way. In this paper, in the case when n = m = 1 , the ground ring is ℂ , and q ∈ ℂ is a 4 k -th root of unity (k ≥ 2 ), we show that φ is not injective.
中文翻译:
Kauffman 支架绞纱模块的连接总和和非注入性
用于把手H G 属G , Przytycki 研究了(考夫曼支架)绞纱模块𝒮 q ( H n # H 米 ) 连接总和的H n # H 米 在q . 他的结果之一是,在这种情况下,1 - q ķ 是可逆的任何ķ ≠ 0 , 同态φ : 𝒮 q ( H n ⊔ H 米 ) → 𝒮 q ( H n # H 米 ) 是同构,由自然方式诱导而来。在本文中,当n = 米 = 1 ,接地环为ℂ , 和q ∈ ℂ 是一个4 ķ - 统一的根 (ķ ≥ 2 ),我们证明了φ 不是单射的。
更新日期:2021-05-05
中文翻译:
Kauffman 支架绞纱模块的连接总和和非注入性
用于把手