Intrinsic symmetry groups of links
نویسندگان
چکیده
The set of isotopy classes ordered n-component links in the 3-sphere is acted on by symmetric group via permutation components. intrinsic symmetry link, S(L), defined to be elements that preserve type L as an unoriented link. study these groups was initiated 1969, but question whether or not every subgroup arises intrinisic some link has remained open. We provide counterexamples; particular, if n > 5, then there does exist for which S(L) alternating group.
منابع مشابه
The 27 Possible Intrinsic Symmetry Groups of Two-Component Links
We consider the “intrinsic” symmetry group of a two-component link L, defined to be the image Σ(L) of the natural homomorphism from the standard symmetry group MCG(S, L) to the product MCG(S) × MCG(L). This group, first defined by Whitten in 1969, records directly whether L is isotopic to a link L′ obtained from L by permuting components or reversing orientations; it is a subgroup of Γ2, the gr...
متن کاملIntrinsic Symmetry Groups of Links with 8 and Fewer Crossings
We present new computations of “intrinsic” symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class group MCG(S, L) or Sym(L) of the pair (S, L). Elements in this symmetry group can (and often do) fix the link and act nontrivially only on its complement. We ignore such elements and focus on the “intrinsic” symmetry group of a link,...
متن کاملGeneralized Intrinsic Symmetry Detection
In this paper, we address the problem of detecting partial symmetries in 3D objects. In contrast to previous work, our algorithm is able to match deformed symmetric parts: We first develop an algorithm for the case of approximately isometric deformations, based on matching graphs of surface feature lines that are annotated with intrinsic geometric properties. The sensitivity to non-isometry is ...
متن کاملSymmetry Groups
Symmetry is a fundamental organizational concept in art as well as science. To develop and exploit this concept to its fullest, it must be given a precise mathematical formulation. This has been a primary motivation for developing the branch of mathematics known as “group theory.” There are many kinds of symmetry, but the symmetries of rigid bodies are the most important and useful, because the...
متن کاملSymmetry Groups
Gauge symmetries: These are local symmetries that act differently at each space-time point x = (t,x) . They create particularly stringent constraints on the structure of a theory. For example, gauge symmetry automatically determines the interaction between particles by introducing bosons that mediate the interaction. All current models of elementary particles incorporate gauge symmetry. (Detail...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2023
ISSN: ['1472-2739', '1472-2747']
DOI: https://doi.org/10.2140/agt.2023.23.2347