相关论文: Cobordism of G-manifolds

In this paper we compute homotopical bordism rings $MU^G_*$ for abelian compact Lie groups G, giving explicit generators and relations. The key constructions are operations on equivariant bordism which should play an important role in…

We calculate the cobordism ring $\Omega^{C_2}_*$ of stably almost complex manifolds with involution, and investigate the $C_2$-spectrum $\Omega_{C_2}$ which represents it. We introduce the notion of a geometrically oriented $C_2$-spectrum,…

We define four distinct oriented bivariant theories associated with algebraic cobordism in its two versions (the axiomatic $\Omega$ and the geometric $\omega$), when applied to quasi-projective varieties over a field $k$. Specifically, we…

We compute the equivariant (stable) complex cobordism ring $(MU_G)_*$ for finite abelian groups $G$.

We give a complete calculation of the cobordism ring of stably almost complex $C_p$-manifolds in terms of generators and relations. We also compare these generators with the geometrically-defined generators obtained by Kosniowski.

Let $\mathcal{N}_*$ be the unoriented cobordism algebra, let $G=(\Z_2)^n$ and let $Z_*(G)$ denote the equivariant cobordism algebra of $G$-manifolds with finite stationary point sets. Let $\epsilon_* :Z_*(G) \to \mathcal{N}_*$ be the…

In this paper we compute homotopical equivariant bordism for the group ${\bf Z/2}$, namely $MO^{\bf Z/2}$, geometric equivariant bordism $\Omega^{\bf Z/2}_*$, and their quotient as modules over geometric bordism. This quotient is a module…

We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any…

We calculate geometric and homotopical (or stable) bordism rings associated to semi-free $S^1$ actions on complex manifolds, giving explicit generators for the geometric theory. The classification of semi-free actions with isolated fixed…

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.

In this paper, we calculate the coefficient ring of equivariant Thom complex cobordism for the symmetric group on three elements. We also make some remarks on general methods of calculating certain pullbacks of rings which typically occur…

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of…

We introduce an equivariant algebraic cobordism theory \Omega^G for algebraic varieties with G-action, where G is a split diagonalizable group scheme over a field k. It is done by combining the construction of the algebraic cobordism theory…

We compute the cohomology of the subalgebra $A^{C_2}(1)$ of the $C_2$-equivariant Steenrod algebra $A^{C_2}$. This serves as the input to the $C_2$-equivariant Adams spectral sequence converging to the $RO(C_2)$-graded homotopy groups of an…

Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…

We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…

Given a real arrangement $A$, the complement $M(A)$ of the complexification of $A$ admits an action of $\mathbb{Z}_2$ by complex conjugation. We define the equivariant Orlik-Solomon algebra of $A$ to be the $\mathbb{Z}_2$-equivariant…

We show that the theory of stable complex $G$-cobordisms, for a torus $G$, is embedded into the theory of stable complex $G$-cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of…

We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…