Calculating the fundamental group of an orbit space
نویسندگان
چکیده
منابع مشابه
The Orbit Space of a Kleinian Group: Riley's Modest Example
In the previous paper, Robert Riley [4] and his computer file Poincaré found a fundamental domain for the action of a discrete group G of isometries of hyperbolic space H3 generated by three parabolics. In this paper, we show that the orbit space H3/G is homeomorphic to a complement 53 — k*, where k* is k union a point and where k is the (3,3,3) pretzel knot. Furthermore, HI 3/G is equipped wit...
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In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...
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For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental SL-invariant function that relates the coordinate ring of the orbit with the coordinate ring of its closure. For the power sums we can write down this fundam...
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Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...
متن کاملThe fundamental groupoid of the quotient of a Hausdorff space by a discontinuous action of a discrete group is the orbit groupoid of the induced action
The main result is that the fundamental groupoid of the orbit space of a discontinuous action of a discrete group on a Hausdorff space which admits a universal cover is the orbit groupoid of the fundamental groupoid of the space. We also describe work of Higgins and of Taylor which makes this result usable for calculations. As an example, we compute the fundamental group of the symmetric square...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0637181-x