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Relevant bibliographies by topics / Classifying spaces, homology, knots

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Journal articles

Academic literature on the topic 'Classifying spaces, homology, knots'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Classifying spaces, homology, knots"

1

VERSHININ, VLADIMIR V. "ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION." Journal of Knot Theory and Its Ramifications 10, no. 05 (2001): 795–812. http://dx.doi.org/10.1142/s0218216501001165.

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Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. The group of virtual braids on n strings VBn and its Burau representation to GLnℤ[t,t-1] also can be considered. The homological properties of the series of groups VBn and its Burau representation are studied. The following splitting of infinite loop spaces is proved for the plus-construction of the classifying space of the virtual braid group on the infinite number of strings: [Formula: see text] where Y is an infinite loop space. Connections with K*ℤ are discussed.

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2

Aceto, Paolo, Daniele Celoria, and JungHwan Park. "Rational cobordisms and integral homology." Compositio Mathematica 156, no. 9 (2020): 1825–45. http://dx.doi.org/10.1112/s0010437x20007320.

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We consider the question of when a rational homology $3$-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology group injects in the first homology group of any other element in the same class. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite-rank cokernels. Further consequences include a divisibility condition between the determinants of a con

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3

Vassiliev, V. A. "Homology of spaces of knots in any dimensions." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359, no. 1784 (2001): 1343–64. http://dx.doi.org/10.1098/rsta.2001.0838.

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4

KAWAUCHI, AKIO. "ON LINKING SIGNATURE INVARIANTS OF SURFACE-KNOTS." Journal of Knot Theory and Its Ramifications 11, no. 03 (2002): 369–85. http://dx.doi.org/10.1142/s0218216502001688.

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We show that the linking signature of a closed oriented 4-manifold with infinite cyclic first homology is twice the Rochlin invariant of an exact leaf with a spin support if such a leaf exists. In particular, the linking signature of a surface-knot in the 4-sphere is twice the Rochlin invariant of an exact leaf of an associated closed spin 4-manifold with infinite cyclic first homology. As an application, we characterize a difference between the spin structures on a homology quaternion space in terms of closed oriented 4-manifolds with infinite cyclic first homology, so that we can obtain exam

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5

Dembegioti, F., N. Petrosyan, and O. Talelli. "Intermediaries in Bredon (co)homology and classifying spaces." Publicacions Matemàtiques 56 (July 1, 2012): 393–412. http://dx.doi.org/10.5565/publmat_56212_06.

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6

Dwyer, W. G. "Homology decompositions for classifying spaces of finite groups." Topology 36, no. 4 (1997): 783–804. http://dx.doi.org/10.1016/s0040-9383(96)00031-6.

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7

Grandjean, A. R., M. Ladra, and T. Pirashvili. "CCG-Homology of Crossed Modules via Classifying Spaces." Journal of Algebra 229, no. 2 (2000): 660–65. http://dx.doi.org/10.1006/jabr.2000.8296.

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8

Clancy, Maura, and Graham Ellis. "Homology of some Artin and twisted Artin Groups." Journal of K-Theory 6, no. 1 (2009): 171–96. http://dx.doi.org/10.1017/is008008012jkt090.

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AbstractWe begin the paper with a simple formula for the second integral homology of a range of Artin groups. The formula is derived from a polytopal classifying space. We then introduce the notion of a twisted Artin group and obtain polytopal classifying spaces for a range of such groups. We demonstrate that these explicitly constructed spaces can be implemented on a computer and used in homological calculations.

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9

OGASA, EIJI. "SUPERSYMMETRY, HOMOLOGY WITH TWISTED COEFFICIENTS AND n-DIMENSIONAL KNOTS." International Journal of Modern Physics A 21, no. 19n20 (2006): 4185–96. http://dx.doi.org/10.1142/s0217751x06030941.

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In this paper, we study and construct a set of Witten indexes for K, where K is any n-dimensional knot in Sn+2 and n is any natural number. We form a supersymmetric quantum system for K by, first, constructing a set of functional spaces (spaces of fermionic (resp. bosonic) states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Our Witten indexes are topological invariant and they are nonzero in general. These indexes are zero if K is equivalent to a trivial knot. Besides, our Witten indexes restrict to the Alexander polynomials of n-knots, and one of

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10

Joachim, Michael, and Wolfgang Lück. "TopologicalK–(co)homology of classifying spaces of discrete groups." Algebraic & Geometric Topology 13, no. 1 (2013): 1–34. http://dx.doi.org/10.2140/agt.2013.13.1.

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