157 research outputs found
Computing the Krichever genus
Let denote the genus that corresponds to the formal group law having
invariant differential equal to
and let classify the formal group
law strictly isomorphic to the universal formal group law under strict
isomorphism x\CP(x). We prove that on the rational complex bordism ring the
Krichever-H\"ohn genus is the composition .
We construct certain elements in the Lazard ring and give an
alternative definition of the universal Krichever formal group law. We conclude
that the coefficient ring of the universal Krichever formal group law is the
quotient of the Lazard ring by the ideal generated by all , .Comment: 6 pages, revised Journal of Homotopy and Related Structures, 201
Polynomial behavior of the Honda formal group law
This note provides the calculation of the formal group law in modulo
Morava -theory at prime and as an element in
and one application to relevant examples.Comment: 4 pages, submitted in Journal of Homotopy and Related Structure
Affine hom-complexes
For two general polytopal complexes the set of face-wise affine maps between
them is shown to be a polytopal complex in an algorithmic way. The resulting
algorithm for the affine hom-complex is analyzed in detail. There is also a
natural tensor product of polytopal complexes, which is the left adjoint
functor for Hom. This extends the corresponding facts from single polytopes,
systematic study of which was initiated in [6,12]. Explicit examples of
computations of the resulting structures are included. In the special case of
simplicial complexes, the affine hom-complex is a functorial subcomplex of
Kozlov's combinatorial hom-complex [14], which generalizes Lovasz' well-known
construction [15] for graphs.Comment: final version, to appear in Portugaliae Mathematic
Some explicit expressions concerning formal group laws
This paper provides some explicit expressions concerning the formal group
laws of the Brown-Peterson cohomology, the cohomology theory obtained from
Brown-Peterson theory by killing all but one Witt symbol, the Morava -theory
and the Abel cohomology.Comment: 11 page
Complex cobordism modulo -spherical cobordism and related genera
We prove that a sequence of polynomial generators of
-spherical cobordism ring , viewed as a sequance in the complex
cobordism ring \MU_* by forgetful map, is regular. Using the Baas-Sullivan
theory of cobordism with singularities we define a commutative complex oriented
cohomology theory \MU^*_S(-), complex cobordism modulo -spherical
cobordism, with the coefficient ring \MU_*/S. Then any is
also regular in \MU^* and therefore gives a multiplicative complex oriented
cohomology theory \MU^*_{\Sigma}(-). The generators of can be specified
in such a way that for the corresponding cohomology is
identical to the Abel cohomology, previously constructed in \cite{BUSATO}.
Another example corresponding to is classified by the
Krichever-Hoehn complex elliptic genus \cite{KR}, \cite{H} modulo torsion.Comment: 10 page
Polynomial generators of related to to classifying maps of certain formal group laws
This note provides a set of polynomial generators of defined by
the formal group law in spherical cobordism. One aspect is to obtain the genera
on with values in polynomial ring as the restrictions of the
classifying map of the Abel formal group law and the Buchstaber formal group
law. The latter is associated with the Krichever-Hoehn complex elliptic genus.Comment: 11 page
Complex cobordism MU modulo MSU and related genera
This paper presents a commutative complex oriented cohomology theory with
coefficients the quotient ring of complex cobordism MU modulo the
ideal generated by any subsequence of any polynomial generators in special
unitary cobordism MSU viewed as elements in MU by forgetful
map.Comment: 5 page
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