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One-cocycles and knot invariants /

Fiedler, Thomas.

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One-cocycles and knot invariants /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	One-cocycles and knot invariants // Thomas Fiedler, Université Paul Sabatier, France.
作者:	Fiedler, Thomas.
出版者:	Hackensack, NJ :World Scientific, : c2023.,
面頁冊數:	xxvii, 308 p. :ill. ;24 cm.
標題:	Knot theory. -
ISBN:	9789811262999

One-cocycles and knot invariants /
Fiedler, Thomas.

One-cocycles and knot invariants /Thomas Fiedler, Université Paul Sabatier, France. - Hackensack, NJ :World Scientific,c2023. - xxvii, 308 p. :ill. ;24 cm. - Series on knots and everything,v. 730219-9769 ;. - Series on knots and everything ;v. 73..

Includes bibliographical references and index.

"One-Cocycles and Knot Invariants is about classical knots, i.e. smooth oriented knots in three-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used in order to construct combinatorial one-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and of the longitude of the knot. The combinatorial 1-cocycles are then lifts of the well-known Conway polynomial of knots and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots"--

ISBN: 9789811262999US128.00

LCCN: 2022026784Subjects--Topical Terms:

523755
Knot theory.

LC Class. No.: QA612.2 / .F546 2023

Dewey Class. No.: 514/.2242

One-cocycles and knot invariants /
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245 1 0 $a One-cocycles and knot invariants / $c Thomas Fiedler, Université Paul Sabatier, France.
260 # $a Hackensack, NJ : $b World Scientific, $c c2023.
300 $a xxvii, 308 p. : $b ill. ; $c 24 cm.
490 1 $a Series on knots and everything, $x 0219-9769 ; $v v. 73
504 $a Includes bibliographical references and index.
520 # $a "One-Cocycles and Knot Invariants is about classical knots, i.e. smooth oriented knots in three-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used in order to construct combinatorial one-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and of the longitude of the knot. The combinatorial 1-cocycles are then lifts of the well-known Conway polynomial of knots and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots"-- $c Provided by publisher.
650 # 0 $a Knot theory. $3 523755
650 # 0 $a Invariants. $3 555710
650 # 0 $a Combinatorial analysis. $3 523878
830 0 $a Series on knots and everything ; $v v. 73. $3 3645422