共查询到20条相似文献,搜索用时 15 毫秒
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Sylvain Gervais 《Transactions of the American Mathematical Society》1996,348(8):3097-3132
We give a presentation of the mapping class group of a (possibly bounded) surface, considering either all twists or just non-separating twists as generators. We also study certain central extensions of . One of them plays a key role in studying TQFT functors, namely the mapping class group of a -structure surface. We give a presentation of this extension.
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Naoyuki Monden 《Topology and its Applications》2012,159(4):1085-1091
We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other. 相似文献
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Patrick M. Gilmer 《Proceedings of the American Mathematical Society》1999,127(8):2483-2488
We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to and induce linear representations of this group. We show that the denominators of matrices which describe these representations over a cyclotomic field can be restricted in many cases. In this way, we give a proof of the known result that if the surface is a torus with no colored points, the representations have finite image.
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Mariusz Grech 《Discrete Mathematics》2010,310(21):2877-2882
We show that with the exception of four known cases: C3, C4, C5, and , all regular permutation groups can be represented as symmetric groups of boolean functions. This solves the problem posed by A. Kisielewicz in the paper [A. Kisielewicz, Symmetry groups of boolean functions and constructions of permutation groups, J. Algebra 199 (1998) 379-403]. A slight extension of our proof yields the same result for semiregular groups. 相似文献
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Aaron Heap 《Topology》2006,45(5):851-886
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphism, the Birman-Craggs homomorphism, and the Morita homomorphism. 相似文献
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A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism ? on the surface, there is a diffeomorphism on the 4-manifold whose restriction on the surface is ? and which is isotopic to the identity. We investigate a sufficient condition for a smooth 4-manifold M to include flexible knotted surfaces, and introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface. 相似文献
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LinFanMAO YanPeiLIU FengTIAN 《数学学报(英文版)》2005,21(2):225-236
A graph is called a semi-regular graph if its automorphism group action on its ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficient condition for an automorphism of the graph F to be an automorphism of a map with the underlying graph F is obtained. Using this result, all orientation-preserving automorphisms of maps on surfaces (orientable and non-orientable) or just orientable surfaces with a given underlying semi-regular graph F are determined. Formulas for the numbers of non-equivalent embeddings of this kind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, the non-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable and general surfaces are enumerated. 相似文献
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《Discrete Mathematics》2022,345(6):112834
A Cayley graph is said to be an NNN-graph if its automorphism group contains two isomorphic regular subgroups where one is normal and the other is non-normal. In this paper, we show that there exist NNN-graphs among the Cayley graphs for symmetric groups if and only if . 相似文献
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Arthur Soulié 《代数通讯》2020,48(6):2467-2491
AbstractIn this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled Artin groups. On the one hand, the computations are led using semidirect product structures arising naturally from these groups. On the other hand, we compute the stable homology with twisted coefficients by FI-modules. This notably uses a decomposition result of the stable homology with twisted coefficients for pre-braided monoidal categories proved in this paper.Communicated by Jason P. Bell 相似文献
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Asaf Hadari 《Advances in Mathematics》2011,226(4):3282
We extend the definition of algebraic entropy to endomorphisms of affine varieties. We then calculate the algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a pseudo-Anosov mapping class. Our calculations are compatible with all known calculations of the topological entropy of this action. 相似文献
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Lyubashenko?s construction associates representations of mapping class groups Mapg:n of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the category of bimodules over a finite-dimensional factorizable ribbon Hopf algebra H . For any such Hopf algebra we find an invariant of Mapg:n for all values of g and n . More generally, we obtain such invariants for any pair (H,ω), where ω is a ribbon automorphism of H. 相似文献
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Ilya Gorshkov 《代数通讯》2019,47(9):3905-3914
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Nathalie Wahl 《Topology》2004,43(2):343-368
Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages (Invent. Math. 130 (1997) 257; Math. Ann. 317 (2000) 613). The first one uses disjoint union on a suitable cobordism category, whereas the second uses an operad which extends the pair of pants multiplication (i.e. the double loop space structure introduced by Miller, J. Differential Geom. 24 (1986) 1). She conjectured that these two infinite loop space structures were equivalent, and managed to prove that the first delooping are the same. In this paper, we resolve the conjecture by proving that the two structures are indeed equivalent, exhibiting an explicit geometric map. 相似文献