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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Finite Symmetries Of S^4, Weimin Chen Chen, Slawomir Kwasik, Reinhard Shultz
Finite Symmetries Of S^4, Weimin Chen Chen, Slawomir Kwasik, Reinhard Shultz
Weimin Chen
This paper discusses topological and locally linear actions of finite groups on S4. Local linearity of the orientation preserving actions on S4 forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of “exotic” groups G (i.e. G 6⊂ O(5)) on S4 are constructed, and local linearity and stable smoothability of the actions are studied.
G-Minimality And Invariant Negative Spheres In G-Hirzenbruch Surfaces, Weimin Chen Chen
G-Minimality And Invariant Negative Spheres In G-Hirzenbruch Surfaces, Weimin Chen Chen
Weimin Chen
In this paper we initiate a study on the notion of G-minimality of four-manifolds equipped with an action of a finite group G. Our work shows that even in the case of cyclic actions on CP2#CP2, the comparison of G-minimality in the various categories (i.e., locally linear, smooth, symplectic) is already a delicate and interesting problem. In particular, we show that if a symplectic Zn-action on CP2#CP2 has an invariant locally linear topological (−1)-sphere, then it must admit an invariant symplectic (−1)-sphere, provided that n = 2 or n is odd. For the case where n > 2 and even, the …
Fixed-Point Free Circle Actions On 4-Manifolds, Weimin Chen Chen
Fixed-Point Free Circle Actions On 4-Manifolds, Weimin Chen Chen
Weimin Chen
This paper is concerned with fixed-point free S1-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, there are at most finitely many distinct smooth (resp. topological) 4-manifolds which support a fixed-point free smooth (resp. locally linear) S1-action and realize the given group as the fundamental group. A similar statement holds for the number of equivalence classes of fixed-point free S1-actions under some further conditions on the fundamental group. The connection …
On A Notion Of Maps Between Orbifolds Ii. Homotopy And Cw-Complex, Weimin Chen Chen
On A Notion Of Maps Between Orbifolds Ii. Homotopy And Cw-Complex, Weimin Chen Chen
Weimin Chen
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants – the homotopy groups, and (2) an analog of CW-complex theory. As a corollary of this machinery, the classical Whitehead theorem which asserts that a weak homotopy equivalence is a homotopy equivalence is extended to the orbifold category.
On A Theorem Of Peters On Automorphisms Of Kahler Surfaces, Weimin Chen Chen
On A Theorem Of Peters On Automorphisms Of Kahler Surfaces, Weimin Chen Chen
Weimin Chen
For any K¨ahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points and fixed components, C.A.M. Peters [12] showed that this group is trivial except when the K¨ahler surface is of general type and either c21 = 2c2 or c21 = 3c2 holds. Moreover, this group is a 2-group in the former case, and is a 3-group in the latter. The purpose of this note is to give further information about this group. In particular, we show that …
Orbifold Adjunction Formula And Sympletic Corbordisms Between Lens Spaces, Weimin Chen Chen
Orbifold Adjunction Formula And Sympletic Corbordisms Between Lens Spaces, Weimin Chen Chen
Weimin Chen
Each lens space has a canonical contact structure which lifts to the distribution of complex lines on the three-sphere. In this paper, we show that a symplectic homology cobordism between two lens spaces, which is given with the canonical contact structure on the boundary, must be diffeomorphic to the product of a lens space with the unit interval. As one of the main ingredients in the proof, we also derive in this paper the adjunction and intersection formulae for pseudoholomorphic curves in an almost complex 4–orbifold, extending the relevant work of Gromov and McDuff in the manifold setting.
A Homotopy Theory Of Orbispaces, Weimin Chen Chen
A Homotopy Theory Of Orbispaces, Weimin Chen Chen
Weimin Chen
An orbifold is a singular space which is locally modeled on the quotient of a smooth manifold by a smooth action of a finite group. It appears naturally in geometry and topology when group actions on manifolds are involved and the stabilizer of each fixed point is finite. The concept of an orbifold was first introduced by Satake under the name “V -manifold” in a paper where he also extended the basic differential geometry to his newly defined singular spaces (cf. [32]). The local structure of an orbifold – being the quotient of a smooth manifold by a finite group …
A New Cohomology Theory Of Orbifold, Weimin Chen Chen
A New Cohomology Theory Of Orbifold, Weimin Chen Chen
Weimin Chen
No abstract provided.
Orbifold Quantum Cohomology, Weimin Chen Chen, Yongbin Ruan
Orbifold Quantum Cohomology, Weimin Chen Chen, Yongbin Ruan
Weimin Chen
This is a research announcement on a theory of Gromov-Witten invariants and quantum cohomology of symplectic or projective orbifolds. Our project started in the summer of 98 where our original motivation was to study the quantum cohomology under singular flops in complex dimension three. In this setting, we allow our three-fold to have terminal singularities which can be deformed into a symplectic orbifold. We spent the second half of 98 and most of spring of 99 to develop the foundation of Gromov-Witten invariants over orbifolds, including the key conceptual ingredient — the notion of good map. In the April of …