Hasil untuk "math.AT"

David Popović

This expository article gives a thorough and well-motivated account of the proof of the nilpotence theorem by Devinatz-Hopkins-Smith.

William Balderrama

We compute the $RO(C_2)$-graded Green functor $\underlineπ_\star L_{KU_{C_2}/(2)}S_{C_2}$.

Roman Mikhailov

A description of the derived functors of Lie functors for free abelian groups is given.

Luis Montejano

An equivalent but useful version on the Homological Nerve Theorem is proved.

Fang Sun

If a fintie group G acts topologically and faithfully on R^3, then G is a subgroup of O(3)

Slawomir Kwasik, Fang Sun

If a finite group acts topologically, faithfully and orientation preservingly on R^3, then it is isomorphic to a subgroup of SO(3).

John Rognes

Notes for the author's MSRI lecture in January 2014.

Holger Reeker

This paper works towards a K(1)-local multiplicative splitting of SU-bordism.

Andre Henriques

These are the notes of a lecture held by Michael Hopkins in march 2007, at the Talbot workshop.

Tornike Kadeishvili

In the rational cohomology of a 1-connected space a structure of $C_{\infty}$-algebra is constructed and it is shown that this object determines the rational homotopy type

Stephen Semmes

The special case of closed subsets of C^n is briefly discussed.

Lewis Bowen

In Thurston's notes, he gives two different definitions of the Gromov norm (also called simplicial volume) of a manifold and states that they are equal but does not prove it. Gromov proves it in the special case of hyperbolic manifolds as a consequence of his proof that simplicial volume is proportional to volume. We give a proof for all differentiable manifolds. This version corrects a few typos in an earlier version and formally proves the theorem for differentiable manifolds rather than locally finite simplicial complexes (but very few actual changes have been made).

Gil R. Cavalcanti

We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. We study implications of the `dd^c-lemma' in the generalized complex setting. Similarly to the standard dd^c-lemma, its generalized version induces a decomposition of the cohomology of a manifold and causes the degeneracy of the spectral sequence associated to the splitting d = \del + \delbar at E_1. But, in contrast with the dd^c-lemma, its generalized version is not preserved by symplectic blow-up or blow-down (in the case of a generalized complex structure induced by a symplectic structure) and does not imply formality.

Jie Wu

We give a combinatorial description of homotopy groups of $ΣK(π,1)$. In particular, all of the homotopy groups of the $3$-sphere are combinatorially given.

Ieke Moerdijk

This is an introduction to gerbes for topologists, with emphasis on non-abelian cohomology.

Daniel Dugger

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

Jie Wu

We give some formulas of the James-Hopf maps by using combinatorial methods. An application is to give a product decomposition of the spaces $ΩΣ^2(X)$.

Jie Wu

We give a specific product decomposition of the base-point path connected component of the triple loop space of the suspension of the projective plane.

Michael Atiyah

A cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n).

Alejandro Adem, James F. Davis

This paper surveys some results and methods in topological transformation groups.