Graph Complexes with Loops and Wheels

Two-loop part of the rational homotopy of spaces of long embeddings

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216514500187 ◽

2014 ◽

Vol 23 (04) ◽

pp. 1450018 ◽

Cited By ~ 4

Author(s):

Jim Conant ◽

Jean Costello ◽

Victor Turchin ◽

Patrick Weed

Keyword(s):

Rational Homotopy ◽

Graph Complexes ◽

Direct Sum

Arone and Turchin defined graph-complexes computing the rational homotopy of the spaces of long embeddings. The graph-complexes split into a direct sum by the number of loops in graphs. In this paper, we compute the homology of its two-loop part.

Download Full-text

Supersymmetry and cohomology of graph complexes

Letters in Mathematical Physics ◽

10.1007/s11005-018-1123-7 ◽

2018 ◽

Vol 109 (3) ◽

pp. 699-724 ◽

Cited By ~ 1

Author(s):

Serguei Barannikov

Keyword(s):

Graph Complexes

Download Full-text

WI-posets, graph complexes and Z2-equivalences

Journal of Combinatorial Theory Series A ◽

10.1016/j.jcta.2004.12.002 ◽

2005 ◽

Vol 111 (2) ◽

pp. 204-223 ◽

Cited By ~ 12

Author(s):

Rade T. Živaljević

Keyword(s):

Graph Complexes

Download Full-text

On the Simple ℤ2-homotopy Types of Graph Complexes and Their Simple ℤ2-universality

Canadian Mathematical Bulletin ◽

10.4153/cmb-2008-053-9 ◽

2008 ◽

Vol 51 (4) ◽

pp. 535-544 ◽

Cited By ~ 11

Author(s):

Péter Csorba

Keyword(s):

Homotopy Type ◽

Graph Complexes ◽

Homotopy Types ◽

Neighborhood Complex

AbstractWe prove that the neighborhood complex N(G), the box complex B(G), the homomorphism complex Hom(K2, G) and the Lovász complex L(G) have the same simple ℤ2-homotopy type in the sense of Whitehead. We show that these graph complexes are simple ℤ2-universal.

Download Full-text