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Dive into the research topics where Marie-Louise Michelsohn is active.

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Featured researches published by Marie-Louise Michelsohn.


Inventiones Mathematicae | 1993

Algebraic cycles and infinite loop spaces

Charles P. Boyer; H. Blaine LawsonJr.; Paulo Lima-Filho; Benjamin M. Mann; Marie-Louise Michelsohn

SummaryIn this paper we use recent results about the topology of Chow varieties to answer an open question in infinite loop space theory. That is, we construct an infinite loop space structure on a certain product of Eilenberg-MacLane spaces so that the total Chern map is an infinite loop map. An analogous result for the total Stiefel-Whitney map is also proved. Further results on the structure of stabilized spaces of alebraic cycles are obtained and computational consequences are also outlined.


Topology | 2003

Algebraic cycles and the classical groups. I: real cycles

H. Blaine Lawson; Paulo Lima-Filho; Marie-Louise Michelsohn

Abstract The groups of algebraic cycles on complex projective space P (V) are known to have beautiful and surprising properties. Therefore, when V carries a real structure, it is natural to ask for the properties of the groups of real algebraic cycles on P (V) . Similarly, if V carries a quaternionic structure, one can define quaternionic algebraic cycles and ask the same question. In this paper and its sequel the homotopy structure of these cycle groups is completely determined. It turns out to be quite simple and to bear a direct relationship to characteristic classes for the classical groups. It is shown, moreover, that certain functors in K-theory extend directly to these groups. It is also shown that, after taking colimits over dimension and codimension, the groups of real and quaternionic cycles carry E∞-ring structures, and that the maps extending the K-theory functors are E∞-ring maps. This gives a wide generalization of the results in (Boyer et al. Algebraic cycles and infinite loop spaces, Invent. Math. 113 (1993) 373.) on the Segal question. The ring structure on the homotopy groups of these stabilized spaces is explicitly computed. In the real case it is a simple quotient of a polynomial algebra on two generators corresponding to the first Pontrjagin and first Stiefel–Whitney classes. These calculations yield an interesting total characteristic class for real bundles. It is a mixture of integral and mod 2 classes and has nice multiplicative properties. The class is shown to be related to the Z 2 -equivariant Chern class on Atiyahs KR-theory.


Geometry & Topology | 2005

Algebraic cycles and the classical groups II: quaternionic cycles.

H. Blaine Lawson; Paulo Lima-Filho; Marie-Louise Michelsohn

In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to algebraic cycles, establishing a direct relationship to characteristic classes for the classical groups, specially Stiefel-Whitney classes. In this sequel, we establish corresponding results in the case where V has a quaternionic structure. The determination of the homotopy type of quaternionic algebraic cycles is more involved than in the real case, but has a similarly simple description. The stabilized space of quaternionic algebraic cycles admits a nontrivial infinite loop space structure yielding, in particular, a delooping of the total Pontrjagin class map. This stabilized space is directly related to an extended notion of quaternionic spaces and bundles (KH-theory), in analogy with Atiyahs real spaces and KR-theory, and the characteristic classes that we introduce for these objects are nontrivial. The paper ends with various examples and applications.


Mathematische Zeitschrift | 2017

Algebraic cycles representing cohomology operations

Marie-Louise Michelsohn

In this paper we will show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg–MacLane spaces


Proceedings of The London Mathematical Society | 1996

Algebraic Cycles and Equivariant Cohomology Theories

H. Blaine Lawson; Paulo Lima-Filho; Marie-Louise Michelsohn


Inventiones Mathematicae | 1984

Embedding and surrounding with positive mean curvature

H. Blaine Lawson; Marie-Louise Michelsohn

{\mathcal K}_{2q}\equiv K(\mathbf Z,{2}) \times K(\mathbf Z,{4}) \times \cdots \times K(\mathbf Z,{2q})


Inventiones Mathematicae | 1984

Approximation by positive mean curvature immersions: frizzing

H. Blaine Lawson; Marie-Louise Michelsohn


Archive | 1990

Spin Geometry (PMS-38)

H. Blaine Lawson; Marie-Louise Michelsohn

K2q≡K(Z,2)×K(Z,4)×⋯×K(Z,2q) have models which are limits of complex projective varieties. Precisely, we have


Archive | 1990

IV. Applications in Geometry and Topology

H. Blaine Lawson; Marie-Louise Michelsohn


Archive | 1990

I. Clifford Algebras, Spin Groups and Their Representations

H. Blaine Lawson; Marie-Louise Michelsohn

{\mathcal K}_{2q}= \varinjlim \nolimits _{d\rightarrow \infty }\mathcal C^{q}_{d}(\mathbf P^{n})

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H. Blaine Lawson

State University of New York System

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