## 7 Citations

Bivariant Versions of Algebraic Cobordism

- Mathematics
- 2015

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…

Motivic Milnor classes

- Mathematics
- 2009

The Milnor class is a generalization of the Milnor number, defined as the difference (up to sign) of Chern--Schwartz--MacPherson's class and Fulton--Johnson's canonical Chern class of a local…

Oriented bivariant theory, II: Algebraic cobordism of S-schemes

- MathematicsInternational Journal of Mathematics
- 2019

This is a sequel to our previous paper “Oriented bivariant theory, I”. In 2001, Levine and Morel constructed algebraic cobordism for (reduced) schemes [Formula: see text] of finite type over a base…

Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems

- Mathematics
- 2014

Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In (2) Behrend introduced a Donaldson-Thomas type invariant for a mor-…

Bivariant algebraic cobordism with bundles

- Mathematics
- 2019

The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism where the cycles carry a vector bundle on the source as additional data. We show that, over a field…

Cobordism bicycles of vector bundles.

- Mathematics
- 2019

The main ingredient of the algebraic cobordism of M. Levine and F. Morel is a cobordism cycle of the form $(M \xrightarrow {h} X; L_1, \cdots, L_r)$ with a proper map $h$ from a smooth variety $M$…

## References

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Motivic Milnor classes

- Mathematics
- 2009

The Milnor class is a generalization of the Milnor number, defined as the difference (up to sign) of Chern--Schwartz--MacPherson's class and Fulton--Johnson's canonical Chern class of a local…

HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES

- Mathematics
- 2005

In this paper we study some new theories of characteristic homology classes of singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformationmCy:…

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- Mathematics
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Motivic characteristic classes

- Mathematics
- 2008

Motivic characteristic classes of possibly singular alge braic varieties are ho- mology class versions of motivic characteristics, not clas ses in the so-called motivic (co) homology. This paper is a…

Characteristic classes of mixed Hodge modules

- Mathematics
- 2009

This paper gives an introduction and overview about recent developments on the interaction of the theories of characteristic classes and mixed Hodge theory for singular spaces in the complex…

Motivic Bivariant Characteristic Classes and Related Topics

- Mathematics
- 2012

We have recently constructed a bivariant analogue of the motivic Hirzebruch classes. A key idea is the construction of a suitable universal bivariant theory in the algebraic-geometric (or compact…

Stratifiable maps and topological invariants

- Mathematics
- 1991

Let X and Y be spaces and f: X -Y be a map between them. Then a large family of problems in topology (and geometry) involve the attempt to relate the invariants of X and Y via f. This attempt has…