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92
Quadratic functions in geometry, topology,and mtheory
"... 2. Determinants, differential cocycles and statement of results 5 ..."
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Cited by 109 (4 self)
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2. Determinants, differential cocycles and statement of results 5
Algebraic topology and modular forms
 Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), Higher Ed
, 2002
"... The problem of describing the homotopy groups of spheres has been fundamental to algebraic topology for around 80 years. There were periods when specific computations were important and periods when the emphasis favored theory. Many ..."
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Cited by 53 (3 self)
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The problem of describing the homotopy groups of spheres has been fundamental to algebraic topology for around 80 years. There were periods when specific computations were important and periods when the emphasis favored theory. Many
Twovector bundles and forms of elliptic cohomology
 in Topology, Geometry and Quantum Field Theory, LMS Lecture note series 308
, 2004
"... The work to be presented in this paper has been inspired by several of Professor Graeme Segal’s papers. Our search for a geometrically defined elliptic cohomology theory with associated elliptic objects obviously stems from his Bourbaki seminar [Se88]. Our readiness to form group completions of symm ..."
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Cited by 49 (8 self)
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The work to be presented in this paper has been inspired by several of Professor Graeme Segal’s papers. Our search for a geometrically defined elliptic cohomology theory with associated elliptic objects obviously stems from his Bourbaki seminar [Se88]. Our readiness to form group completions of symmetric monoidal categories
The sigma orientation is an H∞ map
 American Journal of Mathematics
"... Abstract. In [AHS01] the authors constructed a natural map, called the sigma orientation, from the Thom spectrum MU〈6 〉 to any elliptic spectrum in the sense of [Hop95]. MU〈6 〉 is an H ∞ ring spectrum, and in this paper we show that if (E, C, t) is the elliptic spectrum associated to the universal d ..."
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Cited by 29 (2 self)
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Abstract. In [AHS01] the authors constructed a natural map, called the sigma orientation, from the Thom spectrum MU〈6 〉 to any elliptic spectrum in the sense of [Hop95]. MU〈6 〉 is an H ∞ ring spectrum, and in this paper we show that if (E, C, t) is the elliptic spectrum associated to the universal deformation of a supersingular elliptic curve over a perfect field of characteristic p> 0, then the sigma orientation is a map of H ∞ ring spectra.
Algebraic geometry over model categories  A general approach to derived algebraic geometry
, 2001
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Multiplicative orientations of KOtheory and of the spectrum of topological modular forms
"... We describe the space of E∞ spin orientations of KO and the space of E∞ string orientations of tmf. ..."
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Cited by 25 (1 self)
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We describe the space of E∞ spin orientations of KO and the space of E∞ string orientations of tmf.
On topological modular forms of level 3
"... Abstract. We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the “building complex” associated to level 3 structures at the prime 2. Finally, we note the existence of a number of connective models of the spectrum TMF(Γ0(3)). ..."
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Abstract. We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the “building complex” associated to level 3 structures at the prime 2. Finally, we note the existence of a number of connective models of the spectrum TMF(Γ0(3)). 1.
Brave New Algebraic Geometry and global derived moduli spaces of ring spectra
, 2008
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Varieties and local cohomology for chromatic group cohomology rings
 Topology
, 1999
"... where E is a suitable complete periodic complex oriented theory and G is a finite group: we describe its variety in terms of the formal group associated to E, and the category of abelian psubgroups of G. Our results considerably extend those of HopkinsKuhnRavenel [16], and this enables us to obta ..."
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Cited by 19 (11 self)
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where E is a suitable complete periodic complex oriented theory and G is a finite group: we describe its variety in terms of the formal group associated to E, and the category of abelian psubgroups of G. Our results considerably extend those of HopkinsKuhnRavenel [16], and this enables us to obtain information about the associated homology of BG. For example if E is the complete 2periodic version of the JohnsonWilson theory E(n) the irreducible components of the variety of the quotient E (BG)=I k by the invariant prime ideal I k = (p; v 1; : : : ; v k\Gamma1) correspond to conjugacy classes of abelian psubgroups of rank n \Gamma k. Furthermore, if we invert v k the decomposition of the variety into irreducible pieces corresponding to minimal primes becomes a decomposition