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2017 | OriginalPaper | Buchkapitel

Configuration Space Integrals: Bridging Physics, Geometry, and Topology of Knots and Links (Commentary on [106], [108], [109])

verfasst von : Ismar Volić

Erschienen in: Raoul Bott: Collected Papers

Verlag: Springer International Publishing

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Abstract

Early 1990s witnessed an emergence of new techniques and points of view in the study of spaces of knots and spaces of embeddings more generally. One of the most exciting developments was the introduction of finite type or Vassiliev knot invariants [Vas90]. To explain, any knot invariant V can be extended to singular knots with n transverse double points via the repeated use of the Vassiliev skein relation

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Vorheriges Kapitel On Raoul Bott’s “On Invariants of Manifold” (Commentary on [106], [107])
Nächstes Kapitel Integral Invariants of 3-Manifolds (Commentary on [111], [114])
Literatur
[AS94]
Scott Axelrod and I. M. Singer. Chern-Simons perturbation theory. II. J. Differential Geom., 39(1):173–213, 1994.MathSciNetCrossRef
[AT14]
Gregory Arone and Victor Turchin. On the rational homology of high-dimensional analogues of spaces of long knots. Geom. Topol., 18(3):1261–1322, 2014.MathSciNetCrossRef
[BC98]
Raoul Bott and Alberto S. Cattaneo. Integral invariants of 3-manifolds. J. Differential Geom., 48(1):91–133, 1998.MathSciNetCrossRef
[BC99]
Raoul Bott and Alberto S. Cattaneo. Integral invariants of 3-manifolds. II. J. Differential Geom., 53(1):1–13, 1999.MathSciNetCrossRef
[BL93]
Joan S. Birman and Xiao-Song Lin. Knot polynomials and Vassiliev’s invariants. Invent. Math., 111(2):225–270, 1993.MathSciNetCrossRef
[BN]
Dror Bar-Natan. Perturbative aspects of the Chern-Simons topological quantum field theory. Ph.D. thesis, Princeton University (1991).
[BN95]
[Bot96]
Raoul Bott. Configuration spaces and imbedding invariants. Turkish J. Math., 20(1):1–17, 1996.MathSciNetMATH
[Bot97]
Raoul Bott. Configuration spaces and imbedding problems. In Geometry and physics (Aarhus, 1995), volume 184 of Lecture Notes in Pure and Appl. Math., pages 135–140. Dekker, New York, 1997.
[BT94]
[Bud07]
[CCRL02]
Alberto S. Cattaneo, Paolo Cotta-Ramusino, and Riccardo Longoni. Configuration spaces and Vassiliev classes in any dimension. Algebr. Geom. Topol., 2:949–1000 (electronic), 2002.MathSciNetCrossRef
[CCRL05]
Alberto S. Cattaneo, Paolo Cotta-Ramusino, and Riccardo Longoni. Algebraic structures on graph cohomology. J. Knot Theory Ramifications, 14(5):627–640, 2005.MathSciNetCrossRef
[CDM12]
S. Chmutov, S. Duzhin, and J. Mostovoy. Introduction to Vassiliev knot invariants. Cambridge University Press, Cambridge, 2012.CrossRef
[CM10]
Alberto S. Cattaneo and Pavel Mnëv. Remarks on Chern-Simons invariants. Comm. Math. Phys., 293(3):803–836, 2010.MathSciNetCrossRef
[CR05]
Alberto S. Cattaneo and Carlo A. Rossi. Wilson surfaces and higher dimensional knot invariants. Comm. Math. Phys., 256(3):513–537, 2005.MathSciNetCrossRef
[FM94]
William Fulton and Robert MacPherson. A compactification of configuration spaces. Ann. of Math. (2), 139(1):183–225, 1994.MathSciNetCrossRef
[GMM89]
E. Guadagnini, M. Martellini, and M. Mintchev. Chern-Simons field theory and link invariants. In Knots, topology and quantum field theories (Florence, 1989), pages 95–145. World Sci. Publ., River Edge, NJ, 1989.
[KKV]
Robin Koytcheff, and Ismar Volić. Milnor invariants of string links, trivalent trees, and configuration space integrals. arXiv 1511.02768.
[KMV13]
Robin Koytcheff, Brian A. Munson, and Ismar Volić. Configuration space integrals and the cohomology of the space of homotopy string links. J. Knot Theory Ramifications, 22(11):1–73, 2013.MathSciNetCrossRef
[Kon94]
Maxim Kontsevich. Feynman diagrams and low-dimensional topology. In First European Congress of Mathematics, Vol. II (Paris, 1992), volume 120 of Progr. Math., pages 97–121. Birkhäuser, Basel, 1994.
[Kon99]
Maxim Kontsevich. Operads and motives in deformation quantization. Lett. Math. Phys., 48(1):35–72, 1999. Moshé Flato (1937–1998).
[Koy09]
Robin Koytcheff. A homotopy-theoretic view of Bott-Taubes integrals and knot spaces. Algebr. Geom. Topol., 9(3):1467–1501, 2009.MathSciNetCrossRef
[KV]
Rafal Komendarczyk and Ismar Volić. On volume-preserving vector fields and finite type invariants of knots. Ergodic Theory and Dynamical Systems, 36(3):832–859, 2016.MathSciNetCrossRef
[Lon04]
Riccardo Longoni. Nontrivial classes in \(H^{{\ast}}(\mathrm{Imb}(S^{1}, \mathbb{R}^{n}))\) from nontrivalent graph cocycles. Int. J. Geom. Methods Mod. Phys., 1(5):639–650, 2004.MathSciNetCrossRef
[LV14]
Pascal Lambrechts and Ismar Volić. Formality of the little N-disks operad. Mem. Amer. Math. Soc., 230(1079):viii+116, 2014.
[Sak08]
Keiichi Sakai. Nontrivalent graph cocycle and cohomology of the long knot space. Algebr. Geom. Topol., 8(3):1499–1522, 2008.MathSciNetCrossRef
[Sak10]
Keiichi Sakai. Configuration space integrals for embedding spaces and the Haefliger invariant. J. Knot Theory Ramifications, 19(12):1597–1644, 2010.MathSciNetCrossRef
[SW12]
Keiichi Sakai and Tadayuki Watanabe. 1-loop graphs and configuration space integral for embedding spaces. Math. Proc. Cambridge Philos. Soc., 152(3):497–533, 2012.MathSciNetCrossRef
[Thu]
Dylan Thurston. Integral expressions for the Vassiliev knot invariants. arXiv:math.AT/0701350.
[Vas90]
V. A. Vassiliev. Cohomology of knot spaces. In Theory of singularities and its applications, volume 1 of Adv. Soviet Math., pages 23–69. Amer. Math. Soc., Providence, RI, 1990.
[Vol06]
Ismar Volić. Finite type knot invariants and the calculus of functors. Compos. Math., 142(1):222–250, 2006.MathSciNetCrossRef
[Vol07]
[Vol13]
Ismar Volić. Configuration space integrals and the cohomology of knot and link spaces. Morfismos, 17(2):1–56, 2013.MathSciNet
[Wat07]
Tadayuki Watanabe. Configuration space integral for long n-knots and the Alexander polynomial. Algebr. Geom. Topol., 7:47–92, 2007.MathSciNetCrossRef
Metadaten
Titel
Configuration Space Integrals: Bridging Physics, Geometry, and Topology of Knots and Links (Commentary on [106], [108], [109])
verfasst von
Ismar Volić
Copyright-Jahr
2017
Buch
Raoul Bott: Collected Papers

Print ISBN: 978-3-319-51779-7

Electronic ISBN: 978-3-319-51781-0

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-51781-0_12