Results 1 to 10 of about 14,510 (111)

Algebraic Topology [PDF]

, 2013
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences.
Robins, Vanessa
core   +1 more source

Spectral Sequences in String Topology [PDF]

, 2010
In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding coproduct and ...
Cohen, Cohen, Conner, Elmendorf, Félix, Jakob, Kreck, Lennart Meier, Milnor, Quinn, Vigué-Poirrier, Wall   +11 more
core   +3 more sources

Mathematical Models of Abstract Systems: Knowing abstract geometric forms [PDF]

, 2013
Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they ...
Marquis, Jean-Pierre
core   +3 more sources

Coarse homology theories

, 2000
In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'.
Baum, Christensen, Gromov, Higson, Paul D Mitchener, Pedersen, Roe, Roe, Yu   +8 more
core   +2 more sources

Quandle cohomology is a Quillen cohomology

, 2018
We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectively. We also explain how this makes available the entire range of tools that
Szymik, Markus
core   +1 more source

Open-closed field theories, string topology, and Hochschild homology

, 2009
In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal, Costello, and Hopkins and Lurie, on "open-closed topological conformal field theories".
Blumberg, Andrew J., Cohen, Ralph L., Teleman, Constantin   +2 more
core   +2 more sources

Entanglement, space-time and the Mayer-Vietoris theorem

, 2017
Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality.
Patrascu, Andrei T.
core   +1 more source

On the curvature of vortex moduli spaces [PDF]

, 2013
We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric powers of the ...
A Bertram, A Bertram, A Hatcher, A Jaffe, A Mattuck, A Sen, B Collie, DMA Stuart, E Arbarello, F Fang, G Segal, I Biswas, I Biswas, I Biswas, I Biswas, I Biswas, I Biswas, I Moss, IAB Strachan, IG Macdonald, JM Baptista, K Cieliebak, LA Takhtajan, M Itoh, Marcel Bökstedt, MG Eastwood, N Manton, N Mok, NJ Hitchin, NJ Hitchin, NM Romão, NM Romão, NS Manton, NS Manton, NS Manton, NS Manton, Nuno M. Romão, O García-Prada, O García-Prada, P Griffiths, S MacLane, S Sethi, SB Bradlow, SB Bradlow, SI Gel’fand, SI Goldberg, SK Donaldson, TM Samols, W Fulton, W Lück   +49 more
core   +2 more sources

A lower bound for coherences on the Brown-Peterson spectrum

, 2009
We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP, at a given prime p and prove that it is at least (2p^2 + 2p - 2)-homotopy commutative.
Baker, Baker, Basterra, Birgit Richter, Bruner, Goerss, Hovey, Hu, Kochman, Kriz, Lewis, McClure, Richter, Robinson, Robinson, Strickland   +15 more
core   +1 more source

I-adic towers in topology

, 2004
A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*.
Baker, Baker, Baker, Boardman, Boardman, Eilenberg, Elmendorf, Goerss, Greenlees, Hovey, Hovey, Husemoller, Jensen, Mac Lane, Mac Lane, Matsumura, May, Ravenel, Ravenel, Ravenel, Samuel Wüthrich, Weibel   +21 more
core   +4 more sources