Düğüm teorisinde yeni invaryantlar
Küçük Resim Yok
Tarih
2006
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Niğde Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalısmada dügüm ve halkaların polinom invaryantları bir diyagramatik yaklasımla incelendi. Önce, Parantez polinomu bir diyagramatik yolla tanıtıldı ve burulma sayısı ile normalize edildi. Normalize edilmis parantez polinomu ile Jones polinomu arasındaki iliski verildi. Sonra alterne dügümlerle ilgili bazı aktif tahminler Parantez polinomu hatırlanarak ispatlandı. Jones polinomu ve onunla iliskili cebir bu parantez modeli yardımıyla insa edildi. Aynı zamanda Jones polinomunun genellestirmeleri de tartısıldı. Son olarak, Parantez polinomu ile graf teorisi ve istatistiksel fizik arasındaki iliski incelendi. Bu baglamda Kare parantez bir düzlemsel graf için Dikromatik polinoma özellestirildi. Ve istatistiksel fizikteki potts model için parçalı fonksiyon parantez modeli kullanılarak ifade edildi. Aynı zamanda parantez modeli graflar için Tutte polinomunda da uygulandı. Anahtar Kelimeler: Parantez Polinomu, Jones Polinomu, Genellestirilmis Polinom, Alterne Dügümler, Klasik Dügüm Baglamları, Karısık Cebir, Graf, Dikromatik Polinom, Tutte Polinomu.
In this study, the polynomial invariants of knots and links are investigated with a diagrammatic approach. Firstly, the bracket polynomial is introduced in a diagrammatic way and it is normalized by its twist number. The relations between the normalized bracket polynomial and the Jones polynomial are given. Next, some old conjectures about alternating knots are proved by using the bracket polynomial. The Jones polynomial and its associated algebra are constructed by this bracket model. The generalizations of the Jones polynomial are also discussed. Finally, the relations between the bracket polynomial and graph theory and statistical physics are investigated. Hence, the square bracket is specialized the dichromatic polynomial for a planar graph, and the partition function for the potts model in statistical physics is expressed by using bracket model. Also, the bracket model is applicated the tutte polynomial for graphs. Key Words: Bracket Polynomial, Jones Polynomial, Generalized Polynomial, Alternating Knots, Classic Knot Conjectures, Mixed Algebra, Graphs, Dichromatic Polynomial, Tutte Polynomial.
In this study, the polynomial invariants of knots and links are investigated with a diagrammatic approach. Firstly, the bracket polynomial is introduced in a diagrammatic way and it is normalized by its twist number. The relations between the normalized bracket polynomial and the Jones polynomial are given. Next, some old conjectures about alternating knots are proved by using the bracket polynomial. The Jones polynomial and its associated algebra are constructed by this bracket model. The generalizations of the Jones polynomial are also discussed. Finally, the relations between the bracket polynomial and graph theory and statistical physics are investigated. Hence, the square bracket is specialized the dichromatic polynomial for a planar graph, and the partition function for the potts model in statistical physics is expressed by using bracket model. Also, the bracket model is applicated the tutte polynomial for graphs. Key Words: Bracket Polynomial, Jones Polynomial, Generalized Polynomial, Alternating Knots, Classic Knot Conjectures, Mixed Algebra, Graphs, Dichromatic Polynomial, Tutte Polynomial.
Açıklama
Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı
Anahtar Kelimeler
Matematik, Mathematics
