scholarly journals Tropical curves, graph complexes, and top weight cohomology of $\mathcal {M}_g$

2020 ◽  
pp. 1
Author(s):  
Melody Chan ◽  
Søren Galatius ◽  
Sam Payne
Keyword(s):  
Tropical Curves ◽  
Graph Complexes

scholarly journals Computing complex and real tropical curves using monodromy

2019 ◽  
Vol 223 (12) ◽  
pp. 5232-5250
Author(s):  
Danielle A. Brake ◽  
Jonathan D. Hauenstein ◽  
Cynthia Vinzant
Keyword(s):  
Tropical Curves

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

2014 ◽  
Vol 23 (04) ◽  
pp. 1450018 ◽  
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.

scholarly journals Supersymmetry and cohomology of graph complexes

2018 ◽  
Vol 109 (3) ◽  
pp. 699-724 ◽  
Author(s):  
Serguei Barannikov
Keyword(s):  
Graph Complexes

scholarly journals WI-posets, graph complexes and Z2-equivalences

2005 ◽  
Vol 111 (2) ◽  
pp. 204-223 ◽  
Author(s):  
Rade T. Živaljević
Keyword(s):  
Graph Complexes

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

2008 ◽  
Vol 51 (4) ◽  
pp. 535-544 ◽  
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.

scholarly journals Graph Complexes in Deformation Quantization

2005 ◽  
Vol 73 (3) ◽  
pp. 193-208 ◽  
Author(s):  
Domenico Fiorenza ◽  
Lucian M. Ionescu
Keyword(s):  
Deformation Quantization ◽  
Graph Complexes

scholarly journals Refined curve counting with tropical geometry

2015 ◽  
Vol 152 (1) ◽  
pp. 115-151 ◽  
Author(s):  
Florian Block ◽  
Lothar Göttsche
Keyword(s):  
Tropical Geometry ◽  
Ruled Surfaces ◽  
Plane Curves ◽  
Toric Surfaces ◽  
Formula One ◽  
Tropical Curves ◽  
Tropical Curve ◽  
Severi Variety ◽  
Floor Diagrams

The Severi degree is the degree of the Severi variety parametrizing plane curves of degree $d$ with ${\it\delta}$ nodes. Recently, Göttsche and Shende gave two refinements of Severi degrees, polynomials in a variable $y$, which are conjecturally equal, for large $d$. At $y=1$, one of the refinements, the relative Severi degree, specializes to the (non-relative) Severi degree. We give a tropical description of the refined Severi degrees, in terms of a refined tropical curve count for all toric surfaces. We also refine the equivalent count of floor diagrams for Hirzebruch and rational ruled surfaces. Our description implies that, for fixed ${\it\delta}$, the refined Severi degrees are polynomials in $d$ and $y$, for large $d$. As a consequence, we show that, for ${\it\delta}\leqslant 10$ and all $d\geqslant {\it\delta}/2+1$, both refinements of Göttsche and Shende agree and equal our refined counts of tropical curves and floor diagrams.

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