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http://www.math.uio.no/$\sim$rognes/kurs/ma422h03/

\head Morava $K$-teori \endhead

\subhead 1. (Ko-)homologi-teorier \endsubhead

Singul{\ae}r homologi.  CW-komplekser.  Cellul{\ae}r homologi.

Homologi med koeffisienter.  Singul{\ae}r kohomologi.  Tor og Ext. De
universelle koeffisient-teoremene.

Eilenberg--Steenrod aksiomene.  Kofibreringer og Puppe-sekvensen.  Grenser
og kogrenser.  Generaliserte homologi-teorier og kohomologi-teorier.

H{\o}yere homotopi-grupper.  Hurewicz-homomorfien.  Hurewicz-teoremet.
Fibreringer.  Freudenthals suspensjonsteorem.  Stabil homotopi.

Topologisk K-teori.  Bordisme.

Kategorien av homologiteorier.  Entydighet for ordin{\ae}r homologi.

Atiyah--Hirzebruch spektralsekvensen.
Konstruksjon og konvergens av spektralsekvenser.

Jevne (ko-)homologi-teorier.  $CP^\infty$.

\subhead 2. Spektra \endsubhead

Brown representabilitet.  Eilenberg--Mac\,Lane rom $K(\pi, n)$.  Spektra.
Representerte (ko-)homologiteorier p{\aa} rom og spektra.

Den stabile homotopi-kategorien.  Triangulert kategori.

\subhead 3. Produkter \endsubhead

Eilenberg--Zilber teoremet.  Paringer i homologi og kohomologi.
Kunneth teoremene.  Cup-produkt i kohomologi.  Koprodukt i
homologi.  Algebraer og koalgebraer.

Multiplikative (ko-)homologi-teorier.  Ring-spektra.

\subhead 4. Operasjoner og kooperasjoner \endsubhead

$E^*E$ og $E_*E$.  Steenrod algebraen. Adams spektralsekvensen.

\subhead 5. Kompleks kobordisme \endsubhead

(Ko-)homologi av $CP^\infty$, $BU$, $MU$.

Den komplekse kobordisme-ringen $MU_*$.

\subhead 6. Formelle gruppelover \endsubhead

\subhead 7. Brown--Peterson spekteret \endsubhead

\subhead Morava--Johnson--Wilson spektrene \endsubhead

\subhead Morava $K$-teori av Eilenberg--Mac\,Lane rom \endsubhead

\subhead $S$-moduler og $S$-algebraer \endsubhead

\subhead Produkter p{\aa} $MU$-moduler \endsubhead

\subhead Hopkins--Kuhn--Ravenel karakter-teori \endsubhead

\subhead $A_\infty$-produkter p{\aa} $MU$-moduler \endsubhead

\subhead $S$-algebraisk geometri \endsubhead


\Refs\nofrills{Referanser}
\widestnumber\key{HKR00}

\ref \key Ad74
\by Adams, J. F.
\book Stable homotopy and generalised homology
\bookinfo Chicago Lectures in Mathematics
\publ University of Chicago Press
\publaddr Chicago, Ill.-London
\yr 1974
\endref

\ref \key BJ02
\by Baker, Andrew; Jeanneret, Alain
\paper Brave new Hopf algebroids and extensions of $M$U-algebras
\jour Homology Homotopy Appl. \vol 4 \yr 2002 \pages 163--173
\endref

\ref \key Bo99
\by Boardman, J. Michael
\paper Conditionally convergent spectral sequences
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\pages 49--84 \bookinfo Contemp. Math. \vol 239
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\ref \key Ha02
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\book Algebraic topology
\publ Cambridge University Press \publaddr Cambridge \yr 2002
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\ref \key HKR00
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\paper Generalized group characters and complex oriented cohomology theories
\jour J. Amer. Math. Soc. \vol 13 \yr 2000 \pages 553--594
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\ref \key HPS97
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\ref \key HS99
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\book Morava $K$-theories and localisation
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\endref

\ref \key JW75
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\paper $BP$ operations and Morava's extraordinary $K$-theories
\jour Math. Z. \vol 144 \yr 1975 \pages 55--75
\endref

\ref \key La01
\by Lazarev, A.
\paper Homotopy theory of $A^\infty$ ring spectra and applications
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\jour $K$-Theory \vol 24 \yr 2001 \pages 243--281
\endref

\ref \key MM79
\by Madsen, Ib; Milgram, R. James
\book The classifying spaces for surgery and cobordism of manifolds
\bookinfo Annals of Mathematics Studies \vol 92
\publ Princeton University Press \publaddr Princeton, N.J. \yr 1979
\endref

\ref \key Mi58
\by Milnor, John
\paper The Steenrod algebra and its dual
\jour Ann. of Math. (2) \vol 67 \yr 1958 \pages 150--171
\endref

\ref \key Mi60
\by Milnor, J.
\paper On the cobordism ring $\Omega^*$ and a complex analogue. I
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\endref

\ref \key MM65
\by Milnor, John W.; Moore, John C.
\paper On the structure of Hopf algebras.
\jour Ann. of Math. (2) \vol 81 \yr 1965 \pages 211--264
\endref

\ref \key MS74
\by Milnor, John W.; Stasheff, James D.
\book Characteristic classes
\bookinfo Annals of Mathematics Studies, No. 76
\publ Princeton University Press
\publaddr Princeton, N. J. \yr 1974
\endref

\ref \key RW80
\by Ravenel, Douglas C.; Wilson, W. Stephen
\paper The Morava $K$-theories of Eilenberg--Mac Lane spaces and the
Conner--Floyd conjecture
\jour Amer. J. Math. \vol 102 \yr 1980 \pages 691--748
\endref

\ref \key St99
\by Strickland, N. P.
\paper Products on $MU$-modules
\jour Trans. Amer. Math. Soc. \vol 351 \yr 1999 \pages 2569--2606
\endref

\ref \key Wh62
\by Whitehead, George W.
\paper Generalized homology theories
\jour Trans. Amer. Math. Soc.  \vol 102  \yr 1962 \pages 227--283
\endref

\endRefs
\enddocument
