Zobrazeno 1 - 10
of 367
pro vyhledávání: '"Sikora, A. S."'
Autor:
Sikora, Adam S.
We propose conjectural generalizations of the Fermat-Catalan conjecture, the Tijdeman-Zagier conjecture, and of the Fermat Last Theorem, in which powers are replaced by products of integers. We also formulate a new explicit version of the abc conject
Externí odkaz:
http://arxiv.org/abs/2410.21552
We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold $M$ is finitely generated over $\mathbb Z[A^{\pm 1}]$ if and only if $M$ is irreducible and non-Haken. We analyze in detail the character varieties $X(M)$ of such m
Externí odkaz:
http://arxiv.org/abs/2405.18557
The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed $3$-manifolds are finitely generated over $\mathbb Q(A)$. In this paper, we develop a novel method for computing these skein modules. We show th
Externí odkaz:
http://arxiv.org/abs/2305.16188
Publikováno v:
In Construction and Building Materials 8 November 2024 450
Autor:
Santos, Janaina S., Sikora, Mariana S., Trivinho-Strixino, Francisco, Praserthdam, Supareak, Praserthdam, Piyasan
Publikováno v:
In Journal of Water Process Engineering January 2025 69
Autor:
Lê, Thang T. Q., Sikora, Adam S.
We develop a theory of stated SL(n)-skein modules, $S_n(M,N),$ of 3-manifolds $M$ marked with intervals $N$ in their boundaries. They consist of linear combinations of $n$-webs with ends in $N$, considered up to skein relations inspired by the relati
Externí odkaz:
http://arxiv.org/abs/2201.00045
Publikováno v:
In Construction and Building Materials 19 January 2024 412
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 2271-2308
In this paper, we apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces. We show that any alternating link diagram on a surface is skein adequate. We apply our theory to establish the first and second
Externí odkaz:
http://arxiv.org/abs/2008.09895
Autor:
Sikora, Adam S.
Publikováno v:
Can. J. Math.-J. Can. Math. 76 (2024) 707-727
We study systems of $2$-tangle equations which play an important role in the analysis of enzyme actions on DNA strands. We show that every system of framed tangle equations has at most one framed rational solution. Furthermore, we show that the Jones
Externí odkaz:
http://arxiv.org/abs/2005.08162
Autor:
Tuzun, Robert E., Sikora, Adam S.
Extending upon our previous work, we verify the Jones Unknot Conjecture for all knots up to $24$ crossings. We describe the method of our approach and analyze the growth of the computational complexity of its different components.
Comment: 7 pag
Comment: 7 pag
Externí odkaz:
http://arxiv.org/abs/2003.06724