�Z�~�i�[�̂��m�点

�ߌ�R���O�O���`�S���O�O���@���� ���a ���i���H�� �w�U���ʌ������j
��ځFAlgebraic varieties via a deformation of the Kauffman bracket skein module

�u���T�v

Algebraic varieties via a deformation of the Kauffman bracket skein module
���� ���a�i���H�� �w�U���ʌ������j

In this talk, we will introduce an algebraic variety in an affine space $�mathbb{C}^N$ constructed via the Kauffman bracket skein module (KBSM) of a knot exterior. One of the main ideas for the construction of the variety is that the polynomial map from $�mathbb{C}^N$ to itself can be defined by using a representation of the braid group into the endomorphisms of the KBSM of a handlebody. In fact, the algebraic variety turns out to be an invariant of knots in $S^3$. In this talk, we will try to get a better understanding of the variety by focusing on the number of its irreducible components. Then we will see a relationship of the variety with so-called the Casson-Lin invariant defined by X-.S-. Lin, which in fact inspired the above main idea, and moreover a relationship of the variety with the highest degree of the A-polynomial $A_K(M,L)$ in terms of $L$.

Party �㐔�̍\���Ɗ���\��
���{�c ��i�����嗝�w���j

���H�w���ւ̃A�N�Z�X�C�T�P���ق̈ʒu��
http://web.sci.waseda.ac.jp/campus-map/
���Q�Ƃ��Ă��������D

�F�l�̂��z�������҂����Ă���܂��B

---