共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article, we deal with the following two questions. For smooth actions of a given finite group G on spheres S, which smooth manifolds F occur as the fixed point sets in S, and which real G-vector bundles ν over F occur as the equivariant normal bundles of F in S? We focus on the case G is an Oliver group and answer both questions under some conditions imposed on G, F, and ν. We construct smooth actions of G on spheres by making use of equivariant surgery, equivariant thickening, and Oliver's equivariant bundle extension method modified by an equivariant wegde sum construction and an equivariant bundle subtraction procedure. 相似文献
2.
We construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or cyclic isotropy sets. All
such actions are not compatible with any symplectic form on the manifold in question. In order to cover the case of non-symplectic
fixed point sets, we use two smooth 4-manifolds (one symplectic and one non-symplectic) which become diffeomorphic after taking
the products with the 2-sphere. The second type of actions is obtained by constructing smooth circle actions on spheres with
non-symplectic cyclic isotropy sets, which (by the equivariant connected sum construction) we carry over from the spheres
on products of 2-spheres. Moreover, by using the mapping torus construction, we show that periodic diffeomorphisms (isotopic
to symplectomorphisms) of symplectic manifolds can provide examples of smooth fixed point free circle actions on symplectic
manifolds with non-symplectic cyclic isotropy sets. 相似文献
3.
Krzysztof Pawaowski 《K-Theory》1998,13(1):41-55
The paper presents a procedure for constructing smooth actions of finite perfect groups on spheres with fixed point sets having certain prescribed properties (Theorem A); in particular, having any prescribed configuration of Chern and Pontryagin numbers (Corollary C). The main ingredients used are equivariant thickening and equivariant surgery. 相似文献
4.
Masaharu Morimoto 《K-Theory》1998,15(1):13-32
The paper gives a tool to delete and insert fixed point manifolds for smooth actions of finite Oliver groups on spheres and disks. A similar result was already given in a joint article with E. Laitinen and K. Pawaowski for those of finite nonsolvable groups on spheres. It is useful in classifying smooth actions on spheres from the view point of fixed point data. The methods employed in the present paper are equivariant surgery and equivariant connected sum associated with elements in the Burnside ring. The idea of killing surgery obstructions is as follows: Let G be a finite group not of prime power order, C a contractible, finiteG CW complex, and an element in a K theoretic group arising as an obstruction class of geometric object f. It often holds that (1-[C])m becomes trivial for large integers m where [C] is the element represented byC in the Burnside ring (G). One expects that the algebraic object (1 - [C])m is realizable as the obstruction class of G connected sum of f's related to (1 - [C])m. Since it is true for the case here, we can kill the obstruction by taking G connected sum off's 相似文献
5.
Reinhard Schultz 《manuscripta mathematica》1985,51(1-3):171-199
If p is an odd prime and F is the fixed point set of a smooth Zp action on Sn or Dn, then F is a smooth manifold with a unitary structure. Conversely; most Zp homology disks or spheres with unitary structures are fixed point sets of smooth Zp actions on Dn or Sn for suitable n. The results of this paper show that an arbitrary oriented mod p homology disk or sphere is the fixed point set of a smooth Zp action on some Z[l/2]-homology disk or sphere. This result is in general the best possible.Partially supported by NSF Grants MCS 81-04852 and MCS 83-00669 相似文献
6.
Anand DESSAI 《Frontiers of Mathematics in China》2016,11(5):1151-1187
We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry. 相似文献
7.
M. Brion 《Transformation Groups》1997,2(3):225-267
We study Edidin and Graham's equivariant Chow groups in the case of torus actions. Our main results are: (i) a presentation of equivariant Chow groups in terms of invariant cycles, which shows how to recover usual Chow groups from equivariant ones; (ii) a precise form of the localization theorem for torus actions on projective, nonsingular varieties; (iii) a construction of equivariant multiplicities, as functionals on equivariant Chow groups; (iv) a construction of the action of operators of divided differences on theT-equivariant Chow group of any scheme with an action of a reductive group with maximal torusT. We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations. In particular, we obtain a presentation of the Chow ring of any smooth, projective spherical variety. 相似文献
8.
We investigate what information on the orbit type stratification of a torus action on a compact space is contained in its rational equivariant cohomology algebra. Regarding the (labelled) poset structure of the stratification, we show that equivariant cohomology encodes the subposet of ramified elements. For equivariantly formal actions, we also examine what cohomological information of the stratification is encoded. In the smooth setting, we show that under certain conditions—which in particular hold for a compact orientable manifold with discrete fixed point set—the equivariant cohomologies of the strata are encoded in the equivariant cohomology of the manifold.
相似文献9.
10.
We show that the well-known fact that the equivariant cohomology (with real coefficients) of a torus action is a torsion-free
module if and only if the map induced by the inclusion of the fixed point set is injective generalises to actions of arbitrary
compact connected Lie groups if one replaces the fixed point set by the set of points with isotropy rank equal to the rank
of the acting group. This is true essentially because the action on this set is always equivariantly formal. In case this
set is empty we show that the induced action on the set of points with highest occuring isotropy rank is Cohen-Macaulay. It
turns out that just as equivariant formality of an action is equivalent to equivariant formality of the action of a maximal
torus, the same holds true for equivariant injectivity and the Cohen-Macaulay property. In addition, we find a topological
criterion for equivariant injectivity in terms of orbit spaces. 相似文献
11.
This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.Partially supported by the N.S.F. 相似文献
12.
Hans Scheerer 《manuscripta mathematica》1971,4(2):99-134
In this paper we investigate transitive actions of compact connected Lie groups on certain spaces X which are not spheres, whose dimension is not too small and whose rational cohomology algebra is an exterior algebra on homogeneous generators of odd degree. In case X is a simply connected classical group, a 3-connected real or a 5-connected complex or a quaternionic Stiefel manifold, we obtain (in principle) the classification of the transitive actions on X up to equivariant homeomorphism. 相似文献
13.
Courtney M. Thatcher 《Geometriae Dedicata》2010,148(1):391-415
In this paper we consider free actions of large prime order cyclic groups on the product of any number of spheres of the same
odd dimension and on products of two spheres of differing odd dimensions. We require only that the action be free on the product
as a whole and not each sphere separately. In particular we determine equivariant homotopy type, and for both linear actions
and for even numbers of spheres the simple homotopy type and simple structure sets. The results are compared to the analysis
and classification done for lens spaces. Similar to lens spaces, the first k-invariant generally determines the homotopy type of many of the quotient spaces, however, the Reidemeister torsion frequently
vanishes and many of the homotopy equivalent spaces are also simple homotopy equivalent. Unlike lens spaces, which are determined
by their ρ-invariant and Reidemeister torsion, the ρ-invariant here vanishes for even numbers of spheres and linear actions
and the Pontrjagin classes become p-localized homeomorphism invariants for a given dimension. The cohomology classes, Pontrjagin classes, and sets of normal
invariants are computed in the process. 相似文献
14.
In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■. 相似文献
15.
Benoît Kloeckner 《Geometriae Dedicata》2007,125(1):253-270
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it
is known that there exists countably many analytic equivariant compactification of the isometric action on the hyperbolic
plane. In this paper we study the algebraicity of these actions. We get a classification of the algebraic actions of SL(2;R)
on surfaces. In particular, we classify the algebraic equivariant compactifications of the hyperbolic plane.
The online version of the original article can be found under doi:
. 相似文献
16.
Karl Heinz Mayer 《manuscripta mathematica》1989,63(1):99-114
If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory. 相似文献
17.
Benoît Kloeckner 《Geometriae Dedicata》2006,117(1):161-180
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it
is known that there exists countably many analytic equivariant compactification of the isometric action on the hyperbolic
plane. In this paper we study the algebraicity of these actions. We get a classification of the algebraic actions of SL(2,R)
on surfaces. In particular, we classify the algebraic equivariant compactifications of the hyperbolic plane.
An erratum to this article can be found at 相似文献
18.
Julia Weber 《K-Theory》2005,36(1-2):169-207
We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K0 of the category of “ ϕ -endomorphisms of finitely generated free RΠ(G, X)-modules”. We derive results about fixed points of equivariant endomorphisms of cocompact proper smooth G-manifolds.
Received: February 2006 相似文献
19.
Huajian Yang 《Proceedings of the American Mathematical Society》1996,124(6):1941-1947
In this paper, we have, under some conditions on cohomology, that the fixed point set of a smooth involution on a product of spheres is of constant dimension.
20.
We develop an integral version of Deligne cohomology for smooth proper real varieties. For this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded
Gal(\mathbbC/\mathbbR){Gal(\mathbb{C}/{\mathbb{R}})}-equivariant cohomology of Lewis et al. (Bull Am Math Soc (N.S.) 4(2):208–212, 1981), the equivariant counterpart of singular cohomology. The theory is aimed at giving more precise information about the 2-primary
components of regulators. We establish basic properties and give a geometric interpretation for the groups in dimension 2
in weights 1 and 2. 相似文献