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Quadratic functions in geometry, topology, and M-theory

- M. Hopkins, I. Singer
- Mathematics, Physics
- 13 November 2002

We describe an interpretation of the Kervaire invariant of a Riemannian manifold of dimension $4k+2$ in terms of a holomorphic line bundle on the abelian variety $H^{2k+1}(M)\otimes R/Z$. Our results… Expand

On the nonexistence of elements of Kervaire invariant one

- M. Hill, M. Hopkins, D. Ravenel
- Mathematics
- 26 August 2009

We show that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions… Expand

Equivariant K-theory

- M. Hopkins
- 1968

Topological K-theory [2] has many variants which have been developed and exploited for geometric purposes. There are real or quaternionic versions, “Real” K-theory in the sense of [1], equivariant… Expand

Loop groups and twisted K-theory I

- D. Freed, M. Hopkins, C. Teleman
- Mathematics, Physics
- 13 November 2007

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the “Verlinde ring” of its loop group. In this paper we… Expand

Reflection positivity and invertible topological phases

- D. Freed, M. Hopkins
- Physics, Mathematics
- 21 April 2016

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable… Expand

Structured Ring Spectra: Moduli spaces of commutative ring spectra

- P. Goerss, M. Hopkins
- Mathematics
- 2004

Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E∗E is flat over E∗. We wish to address the following question: given a commutative E∗-algebra A in E∗E-comodules,… Expand

GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES

- M. Hopkins, N. Kuhn, D. Ravenel
- Mathematics
- 26 April 2000

Let BG be the classifying space of a finite group G. Given a multiplicative cohomology theory E ⁄ , the assignment G 7i! E ⁄ (BG) is a functor from groups to rings, endowed with induction (transfer)… Expand

Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups

- E. Devinatz, M. Hopkins
- Mathematics
- 2004

Abstract Let G be a closed subgroup of the semi-direct product of the nth Morava stabilizer group Sn with the Galois group of the field extension F p n / F p . We construct a “homotopy fixed point… Expand

Twisted K-theory and loop group representations

- D. Freed, M. Hopkins, C. Teleman
- Mathematics, Physics
- 8 December 2003

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations… Expand

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